Cold, snowy and frosty all the time...hmmm..sounds like the Inuit, Lapps, and other peoples of the Far North.
They hunted caribou and fished the open seas. Very little plant intake; maybe some berries in the Arctic summer.
I think the concept you're looking for is the "growing season." A short growing season of 90 days or less is, by and large, what the Russians, Scandinavians, and Scots dealt with; thus the short list of foods.
Some root veggies will KEEP in cold situations; I personally don't know which ones and for how long.
But nothing that I'm aware of will germinate (sprout and begin to grow) outdoors in harsh winter conditions.
That's why, historically, peoples of the Far North (Inuit, Lapps, Siberian nomads) kept animals (caribou/reindeer/elk), hunted animals, or fished for a living. There was no way to grow food, so they had to herd/hunt it.