Except for hunting. Most non-meat food rots, and i presume meat isn't enough to give all the supplements the body needs. And even if most of them were able to survive through the winter with a meat only diet, could hunters really bring enough to the entire tribe?
So I'm only an amateur historian (like, a bloke with an interest.) But I think I can answer this to at least some extent.
By primitive, I assume you're talking basically about hunter-gatherers, peoples living before agriculture takes a significant hold. This is a world where what you eat and when you eat it is basically determined by the seasons - you won't be likely to eat many apples in february.
So there are a few resources you can collect in the winter, and you're right to say that they're probably mostly meat based and probably not around in abundance. Large game like deer might well work, and fishing for both fish and shellfish would provide you with a source of meat and protein. This probably wasn't super reliable though - one year you bring down lots of game, great! But next year you don't, so what do you do?
If the ground's covered in snow it's unlikely you're gonna get much in the way of fruit and veg aside from some choice winter berries, and possibly some hardy leaves. But pretty much everything else is gonna be dead or buried.
I put it to you that the answer to this problem is storage and preservation. Salting, smoking and drying your food is probably the best bet, since depending on where you're living you might not get temperatures cold enough for dependable freezing. Meat, fish, shellfish, etc. can all be salted and smoked. Hardy root vegetables, like parsnips and beetroots, could probably be dried out so they kept longer, as could any berries. Nuts, of course, require little to no preparation, so they could just be kept as is - if it works for squirrels it can work for us too. They might also have been able to store fruit by making them into something a bit like cider? Or maybe something rather sweeter, if they had some honey? Those are both mostly guesswork though, I've no idea whether or not the techniques for this sort of thing were around at the time.
Then all you need to do is find somewhere to put it, out of reach of the elements as well as any animals that would like to raid your stores. I'd suggest something like a storage pit would work for this kind of thing, with a cover over the top, or maybe a nice deep area of a cave. Keeping stuff cool and dry like that probably went a long way towards keeping it edible.
Ultimately, since meat and fish is probably the easiest to keep and store, the diet of the hunter-gatherer probably looked pretty protein heavy in the winter. But there are definitely a few veg you can store up for a decent amount of time as well. And if you're particularly peckish you can go forage for some little alpine strawberries - lovely! (Not sure how this works outside of Europe, but I imagine the rough gist is the same.)