Layers are the way to go.

1. Long Underwear, a long sleeve breathable undershirt, good WOOL socks
2. A sweater or other medium-thickness top garment.
3. 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).