Some little bits of advise from my experience living here: I won't recommend any particular brands or anything like that, I never use anything fancy or expensive and I've always been fine. Your two greatest concerns should be your hands and feet. They get cold faster than anything else on you by far (ears too I guess but keeping those covered doesn't take much though/is pretty hard to screw up).
Hands - when it's really cold, wear mitts, not gloves. Gloves are not enough and they're not even any more handy. The kind of gloves that might be warm enough to do the job are also going to by necessity be thick enough that you'll need to take them off to pull a trigger, no different than a mitt, not as warm tho.
Feet. If there was a single piece of hunting equipment, we're talking guns, ammo, clothing, knives and such, all of it, that I would say you absolutely cannot get away with using if it's not good, no cheaping out, no compromising, it's your footwear. The most important piece of winter clothing you'll buy is your boots. Lousy jacket? Cram enough sweaters and long underwear underneath it and you'll be fine (I have in fact done this and been fine). Mitts arent warm enough? It's not ideal but you can cram your hands into your pockets or even right under your shirt against your body for a bit if you find you're in trouble. Again, I have done this in unprepared moments, you'll really grit your teeth when your ice fingers touch your warm torso. But if your feet start to freeze you're out of luck, no tricks, it's just over, you need to just be done for the day and get somewhere warm. Make a point of buying boots a size larger than you wear so you can comfortably wear big wool socks in them.