On a side note, you might be surprised what you can find during the winter, especially in scarcely populated areas. When I was a kid (I grew up on Fox Island, Washington), I'd take a row boat to nearby islands that were too small to have people or large wildlife on them and come across frozen berries of various types.
Roots can be found year round. Many are quite carb heavy, but can be a pain in the *** to get to if the ground is frozen. This can actually serve as an advantage because that keeps animals away from things that you can't get to without digging tools.
Most sea weeds are edible. They won't keep you from starving, but they're nutritious nonetheless.
Almost any grass will have something resembling wild garlic mixed in with it, and it will often remain edible after a freeze.
Could you support a major population off foraged vegetation in the winter? Not a chance. A small tribe, so to speak? Arguably, yes. At the very least, you could supplement other stored goods.