In a mountain enviroment with snow there are no way to be alive 3 weeks with no food, with good luck and warm clothes you can live one week. Altitude and cold eat your body. I know that bc I spent more than 20 years doing alpinism in high and cold mountains.
Discussion
if you can't get to lower ground yeah you are gonna be screwed but fuck sitting in a snow cave waiting to be eaten from drawing straws, i'd take my chances with falling off the side of a cliff over that any day