Layers are the way to go.
- Long Underwear, a long sleeve breathable undershirt, good WOOL socks
- A sweater or other medium-thickness top garment.
- Waterproof snow pants and coat.
Good boots, preferably waterproof if you’ll be in the snow a fair amount. Definitely good so you have better grip on snowy/icy ground. Thin “liner” gloves and thick waterproof gloves to go over those. A warm hat that covers your ears (I really appreciated my trapper hat when I went to Tromsø).
Avoid cotton. Cotton is horrible at insulating if it gets wet, as opposed to wool which can keep you warm while fully drenched.
Good idea, but again: wool socks will stay surprisingly warm even while wet.
If you’re in the arctic circle long enough, it helps to have many options though.