Skammer is very well equipped and knows his stuff.
For you guys on a budget, it can be done somewhat cheaper with bargain fleece, coated or treated (campdry) nylon rainwear and cheap ski bibs and an insulated jacket for camp wear. Of course a pack and a sleeping bag is a necessity for any extended backcountry outing (overnight). Of course a tent is also a great idea, although shelters, are sometimes available in some areas. Take my word for it, most of them suck and are cold, dirty, drafty, and often leak.
Or if your into traveling light, ditch the insulated clothing and use your sleeping bag as an insulated garment in camp (keep it out of the snow and wet).
Fires are great, but firewood is hard to come by in the high country, especially. Don't expect to be comfortable like on the couch at home. At -10 below it just aint gonna happen (no central air or comfy couches in the backcountry). The idea is avoiding frostbite and hypothermia. Get a good insulated pad to go under your sleeping bag. A thermarest is very good, but any closed cell foam pad will work (the thicker the better). If you don't have one, use extra clothes, or your pack under your bag (keeps you off the cold ground).
But you get the basic idea. Layers, that you can put on and take off as your body warms and cools.
Don't skimp on your synthetic underwear or your hat, the heavier the better in the backcountry in winter. After all, better to be too warm and dry than too cold and wet. And you need wind garmets. Either your waterproof jacket/pants, or thin nylon pullover etc. for hiking. Remember, at 10 degrees on the move, you'll most likely be in your underwear only. So bring a pair of nylon shorts to go over your bottoms unless you like sweating, then ending up having to dry out at camp (not a good thing).
And get a decent set of boots made for whatever outdoor pursuit you're anticipate engaging in. And don't forget good wool socks. Liners too if your feet are sensitive. Nothing better or more durable than smartwool hikers. Good gloves can literally keep your hands from feeling like they are freezing off when doing work in camp. Otherwise if they get cold, put them where they will get warm preferably before they turn grey and you get frostbite (down your pants).
And like I pointed out above, you never want to get caught unprepared in the backcountry if possible, especially in winter. Or there's a very good chance you will die, cold and alone. Don't count on a fire. Sometimes it's just not practical or a good idea, especially in the mountains. But a great last resort when nothing else is working, if firewood and conditions make it available.
I can't emphasize the importance of knowing where you're at and where you're going at all times. And if in the high mountains in winter, take a pair of crampons, if you don't like turning back or sliding for miles down landslides, etc..
If you can survive in the mountains in winter, you can survive anywhere.