Ziggy has touched on this, but I just want to clarify before diving into the actual text itself: in terms of your paragraph spacing, you're being inconsistent. There are two ways to space paragraphs: to indent the first line, or to double-space, leaving a line break between the two. What you do here is use a double-spaced line break to separate your major chunks, while using a single line break to break it up at other points, e.g. after a line of dialogue. The result is this:
Frankly, this makes no sense. Why is there a larger gap between 'swallowing his fright' and 'hold up, there'? You can only do one or the other. Either go with single-spaced line breaks and indented first lines, or double space everything. It'll look different, and more spaced out, but consistency is key.
Anyway! That's really neither here nor there; it's got nothing to do with the actual writing. I'm just gonna cover the prologue for now: inside the quote you'll find close-reading notes, with some broader thoughts at the end.
The air was filled with the perpetual dancing of snowflakes  to the angry backing track  of howling wind. The snow did a fine job of hiding the barren landscape,  disguising the dead world under a perfect sheet of white innocence.  It was a lie of sorts, but a lie people chose to believe. No one wanted to clear the persistent snow and reveal the scarred ground that lay comatose beneath.  Ignorance, as they say, is bliss. 
1 – Opening with a description of the weather is a pretty well-worn trope of fiction; a lot of people recommend you steer clear of it, if I remember correctly. If you’re going to do it, you really have to pull out all the stops to make it unique and engaging. ‘Perpetual dancing of snowflakes’ is verging on an interesting image, but there’s something inconsistent about it: do snowflakes really ‘dance’, for example? It’s stretching it a little. First things first, though: unless there’s a real reason to start with passive voice, I’d switch it around. ‘Snowflakes danced in the air...’
2 – Howling wind is not a ‘backing track’. This description – appropriating a technological term used in music/film production etc. – feels out of place.
3 – Multiple issues here. You can’t ‘hide’ a barren landscape, really; it’s either barren or it isn’t. If something hides it, then it’s not barren anymore. Sort of. I get what you’re going for but it’s a little off. Another issue, though, is this: how do we know the landscape is barren? You’re telling us too much. All we see is the snow; anything could be underneath.
4 – Again, telling us too much. This is a nice image – the ‘perfect white sheet’ – but less is more, and that’s all you really need to tell us. It’s definitely not ‘white innocence’; that’s far too in-our-face.
5 – Too broad and generic, and also muddled. A lie ‘of sorts’? Is it or isn’t it? What people? Do they really care about clearing the snow or is all this just a figure of speech?
6 – This line really gives the narrator a sense of character, which I’m not sure is carried through the rest of the piece – begging the question, why does it appear here? I’m not sure it’s necessary for the narration to make this sort of broad, clichéd statement. To what end is it used?
The snow hung in the air like fog,  restricting vision  to just a few feet. Through the haze a figure emerged, materializing into focus like a supernatural deity.  The figure was of a lone man,  trudging through the deep snow with long boots suitable for the task, his movements practiced and fluid.  His body was encased in a set of combat armor, once white but now faded. A long, grey duster atop flapped in the wind. The man’s face was hidden beneath a Power-Armor  helmet spray-painted a metallic white, the eyes dark and lifeless, giving the figure  a robotic appearance. Even his hands were hidden, with gloves that had metal plates attached.
7 – Okay, so we’re back to this again? It’s a nice image, but repetitive. If I’m honest, this is also a stronger opening than the previous one; you could potentially cut out a lot of the first paragraph.
8 – Whose vision? Where are we? What are we looking at?
9 – This is a bit of a nothing simile, because the thing you’re comparing it to – the supernatural deity – is abstract, if nonexistent. It’s also too heavily-laden with the subtext of this character being either supernatural, or a Christ figure, which, if it’s supposed to be foreshadowing, is coming on way too strong.
10 – I’d try to mention this immediately when introducing the figure, as opposed to doubling up on the description.
11 – I don’t think you need to spell out that the boots are ‘suitable for the task’; just tell us what they are. The ‘practiced and fluid’ is nice description, though – it begins hinting at the character, and their preparedness for this world.
12 – Again, I think Ziggy touched on this, but I’m not a fan of this name-dropping stuff. It’s a cop-out. Instead of doing the hard work to describe what we see, you’re just riding the coat-tails of the game, and expecting the reader to know what to picture based on the item.
13 – Now that he’s a man, don’t go back to calling him a ‘figure’. You can’t return to vagueness after becoming specific.
The men  hated gate duty, but they all had to do it. One of the pair  slapped his colleague and nervously nodded toward the incoming man.  Both guards were dressing in simple clothes and basic armor, layered against the cold, with a torn sheet acting as a scarf that wrapped around their necks and faces.
"It can't be," one of the men  mumbled underneath his face-wrap.
"Sweet Jesus, it is... What do you think he wants?"
The guard just shook his head. He reached up with a gloved hand and pulled the scarf down, grimacing against the cold, swallowing his fright.
14 – What men? I thought we were looking at the ‘figure’ walking through the snow?
15 – Seriously, what men are we looking at?
16 – And now we’re looking at the ‘incoming man’? The ‘figure’? There are two issues here. One is that the lack of pronouns makes it extremely difficult to decipher which characters we’re looking at. But the real issue is that you’ve introduced these guards without giving us, for lack of a better term, an ‘establishing shot’ of them being there. We jump from a thinly-described ‘barren wasteland’ of snow, to a figure emerging through the haze, to two abstract men. It’s difficult to get a handle on what mental image we’re supposed to create. It may seem obvious, but – what are they guarding?! They’re on ‘gate duty’. So describe the gate! What’s behind it? Where are we?
17 – Again, more careful selection of pronouns here could save a lot of headache. We’re dealing with three ‘men’, which can get confusing fast. This one should definitely read ‘one of the guards’. More specifically, it would be good to try and distinguish between the two guards, so that when the dialogue begins flowing, we know what’s going on.
“Hold up, there!” he ordered with as much authority as he could manage, despite his nerves. He felt like he was giving an order to God.  Well, he thought, he practically was. 
The lone man slowed, approached and finally stopped, standing a few feet from the guards.
“What’s your business here?” the guard asked.
The man didn’t answer. Instead he just stood there. Through the mask, the guards couldn’t tell if he was staring, but they could feel he was.  They felt the black, soulless eyes reach deep into their hearts, which pounded with anxiety.  The two guards shared a brief look each one wishing for the other do do something.
“No tourists,” the second guard finally said, allowing his arm to fall away from his body slightly. The lone man’s head turned a fraction, likely looking at the guard’s weapon – a long Thermic Lance. His head returned, seeing the other guard with an assault rifle.  Despite the two weapons, he showed no reaction; instead he remained motionless.
Again the guards exchanged glances, but this time the visitor did move. He stepped forward, quickly, his left hand flying out from inside his coat with a Samurai Sword in the gloved fist. The blade arced wide to one side. The guard's eyes went wide.
With no hesitation,  the man thrust the blade forward, piercing through the leather-based armor with a pop, tearing through the layered cloth with a soft ripping sound, and plunging into the guard’s chest cavity a squelch.  The second guard – the one armed with the Thermic Lance  – flinched at seeing the death of his colleague. He lifted his melee weapon and motioned it toward the murderer. 
The man saw the movement, and had expected it. With the guard impaled on his sword, he brought his right hand from his left hip and fired a single shot from his silenced pistol. The bullet hit the guard in the forehead and with a soft puff he fell to the snowy ground. The man withdrew his sword, wiping it on the guard’s clothing, and replaced it in its sheath, which hung on his hip. He holstered his pistol too then crouched and searched the two bodies. 
After taking everything of value,  he turned to enter the settlement. He paused at the door for a moment,  looking back at the fallen men. He turned and once again crouched down, the mechanical sound of his breathing the only sound he made.  He picked up the Thermic Lance and weighed it. Then he spun it round in his hand, first in a circle then a figure-of-eight before swiping it diagonally down and stabbing it outward. With a pleased nod, he picked up the guard’s harness and with it, slung the weapon over his shoulder, holstering it on his back. He then entered the settlement.
18 – Again with the heavy religious imagery. I’m not sure about it.
19 – Be aware that you’ve made the decision to align the reader with the guards’ inner monologues. Is this what you’re going for? Would it be more effective for us to be distanced from them?
20 – This is a nice image.
21 – But this not so much. ‘Black, soulless eyes’ is very bland and obvious description.
22 – We now seem to be privy to the lone man’s thoughts, too, but I’m not getting a strong sense of POV from anyone in this scene. I don’t mean literally in terms of getting their inner monologue, but just in terms of where we’re viewing the scene from: it’s all very vague.
23 – The very act of saying this implies a sense of hesitation. If he doesn’t hesitate, then don’t hesitate in the description. Get straight to it. Have your prose take on the same rhythm as the scene.
24 – The prose here betrays the scene. It seems shocking and unpredictable, but structuring the sentence around three pieces of identical description (with a pop, with a soft ripping sound, with a squelch) becomes quite formulaic, and a little bland.
25 – This recalls the fact that there’s no way to distinguish the guards. You shouldn’t have to butt in halfway through an action scene to remind us that he’s the one ‘armed with the Thermic Lance’ – everything about it slows the scene to a halt.
26 – I don’t think there’s any reason to throw in this extra pronoun here, ‘the murderer’. For one, it confuses matters in a scene where we’re already struggling to convey the characters. More importantly, it implies a sense of judgement on behalf of the guard; that is to say, it’s as though his perception of the lone man has changed, and now he’s saying “you murderer!” But if we’re to assume that this is a cold, ruthless, violent world... well, nothing’s changed, really.
27 – There’s a lot of very, very precise detail here: right hand, left hip etc. It’s a bit too choreographed. Try to just give a sense of the action, rather than describing every tiny detail of it; with so much detail, it’s hard to get a sense of which piece of information is the most important. The best image here, for me, is the guard falling with barely a sound into the snow. I’d focus on that and try to figure out how best to convey it, rather than trying to convey every tiny little motion.
28 – What does he take? This is where I’d like more description: how does he search them, what does he find, etc. It’s an opportunity to tell us about him and the world, as well, especially in terms of what he might leave behind – what does he deem to be of value?
29 – Again, by this point, I feel like we should have a far clearer image of the settlement he is approaching.
30 – This sentence is pretty clumsy, owing to the repetition of the word ‘sound’. Also, re: the mechanical breathing, is he actually a robot, or what? This is intriguing, but a little more specificity would be helpful.
He knew the layout well. Once inside he ducked behind a shack. He wanted to avoid the center of town, where he’d likely be seen. He moved on, knowing his destination and what route to take to avoid confrontation. He could hear the distant chatter, voices he recognized, spoken by men he knew. He skirted the town, staying close to the outer wall, and hidden by the ramshackle buildings that, despite their appearance, were sturdy enough to survive the harsh weather.  The snow was working in his favor, though his footprints might eventually be seen. Perhaps no one would pay attention to them, or the snow might cover them up, but he couldn’t count on that. 
31 – This is a very vague snapshot. We know nothing of the town, there’s barely any detail at all. Now we’re inside and you’re skimming over it even more. It really needs more detail if you’re going to take us inside with the character.
32 – This is another nice image of the snow hiding his footprints; I think you could perhaps elaborate on it a little more. Have it actually come into play in the story, as opposed to just being a brief musing by the character?
His objective stood in front of him after just a couple of minutes of skulking. He watched it  for a moment, making sure there were no patrols nearby. Content, he moved forward and approached the front door, careful to check no one saw him.
33 – Once more, what are we seeing? What is ‘it’? What is the objective? I get the sense that you’re hiding things on purpose, but in this case it feels like a bit of a cheat. If the character sees it, we need to see it.
The door  creaked open and he stepped inside. Two surprised faces stared at him and, for a second, considered questioning his presence.  Before alarm could set in, though, the pistol was out and pointed at the men – who had been sitting at a table, a pack of dirty playing cards slung over the scratched wood.  Without a word, the intruder pointed the men toward the jail cells, which stood at the back of the building and held only one prisoner. The two men stood, intimidated by the metal man and his mechanical breathing. Without a word of protest, and with much fear of the man, they obeyed.
After stripping the men of their guns, and pointing them at the metal bars, he watched them unlock the cell door. He waved them inside with his gun. The man, still nonspeaking, pointed at the only prisoner and crooked his finger. Rather sheepishly, and somewhat weakly, she got to her feet. 
34 – Door of what? What building is it? Where are we?
35 – Now we’re privy to the thoughts of random passers-by. I’d question this.
36 – All this detail comes too late. Tell us what we see – that they’re playing cards at the table – the moment we walk in, not later on.
37 – I think we could do with a quick description of the woman after ‘the only prisoner’, as opposed to revealing who the prisoner is in the next sentence. It’s like you’re trying to cloak her in mystery for just a little longer – but to what end?
The infiltrator  tied the men's hands together and gagged them. Then he turned to the woman and waved for her to follow. While he was imprisoning the captives – the irony of which he found comical  – the woman had retrieved her possessions and dressed in her own clothes. The man, standing by the door and looking out, found it strange that they had kept the items and not sold them on.
He watched for a moment. Then he waved at the female and they exited the building, disappearing into the white mist.
38 – Ziggy liked this, but I’m not a fan. You’re using too many different pronouns to describe the same character, and for me, a little more consistency would work better. Is he the intruder, or the infiltrator, or the lone man, or the metal man, or what?
39 – Signposting irony like this just feels a bit tacky. And it’s not very comical, so it makes me question the character. He seems to be painted as a ruthless wanderer – yet now he finds this situation humorous? I’d think a little harder about what a brief insight into the character’s mind, in this way, tells us about him, and whether it’ll send the right message.
Overall, I think this is well written, and crafted at times with close attention to detail, but it's also quite clumsy in parts. I really, really wanted some more concrete information about what we're seeing, especially in terms of the town – and super-especially once we were inside. You can still do that while retaining an air of mystery and intrigue, if that's what you're going for.
As for hooking us in, I think the very end of the sequence did that well. We're left with four main questions: who's the guy, who's the girl, why's she imprisoned, and why's he come to rescue her? The answer to question two, I assume, comes in the chapter you've just posted; the rest remain, like your proverbial dancing snowflakes, up in the air.
I think this is a strong central hook, but it could do with a little more jeopardy. I wanted to see more of the girl's immediate response, so that her character – and the lone man's, by extension – begins to be elucidated, if only a touch. What's more, I think you spend far too much time building up to this moment; if this rescue/breakout is the crux of the prologue, then the rest is largely irrelevant, and it makes the chapter as a whole feel quite laboured.
I agree with others in that it doesn't feel overly rooted in the Fallout world (a notion that grows in the more recent chapter, but I'll touch on that at a later date). The snow-covered barren landscape more easily recalls The Road than Fallout, but that's not a problem: it's an interesting setting. But this is just a teaser, so it has much room to expand into the established world.
As it is, it's an interesting moment, but it's a little dragged out. If you only take one thing away from everything I've just said going forward, then let it be this: in terms of the pacing of both the scene itself and of the prose, try to pin down what you're going for, and then make everything work towards that. If the scene is supposed to be swift and violent, then describe it as quickly and briefly as possible – make the scene on the page short but sweet, and give the prose just enough detail for us to understand what's going on. Conversely, if the scene is supposed to be slow and reflective, go in the opposite direction: give it some length (unless it's boring, but then you have a problem with the scene) and make the prose a little more contemplative.
As I say, I'll be back asap with a similar reading of the next chapter. Until then, get working on the third!