Hey there, Strive. I'll give you what I can for Alaska, keeping in mind that the Alaska experience shouldn't be carried over to all of North America.
First, lemme throw a few books your way. An easy, basic primer is The Native People of Alaska by Steve Langdon. It's used as a textbook in a lot of intro to Alaska history classes, and it's got a killer bibliography when you're ready to move on. If Langdon's book is too basic for you, try Crossroads of Continents: Cultures of Siberia and Alaska by Fitzhugh and Crowell. It's a hefty book, but it has lots and lots of pictures. For specialized looks, I'll go with The Eskimos of Bering Strait: 1650-1898 by Dorothy Jean Ray and Kodiak Kreol by Gwenn Miller.
Now that we've got the sourcing out of the way, let me add another qualification: I'm going to talk principally about northern, western and southwestern coastal Alaska. There's two main reasons for this: These are areas I feel more comfortable talking about and I don't want to spend an eon writing this.
With that out of the way, let's answer your question. In these areas of Alaska, winter activity was geared toward non-food material production, including clothing and tools.
This isn't to say winter was exclusively for non-food activity, but most food-gathering took place in summer. There were salmon runs, crabs, coastal fishing, seals, walrus, and the odd whale. Jean Ray likes to divide the Bering Strait Natives into three groups: whaling-walrus, caribou, and small sea mammal.
If you're in the whaling-walrus group, you're primarily active in the summer, taking advantage of the sea to get your food. You're probably on an offshore island or living literally on the beach. If you're in the caribou group, you're mainly after caribou and are somewhat inland. If you're a small sea mammal hunter, you're somewhat in between. You rely on the sea, but you're not a fisherman so much. Keep in mind, however, that all three groups are dependent upon the salmon run. That holds true pretty much everywhere in Alaska.
I'm talking about food so much, because that's the factor that drives survival. If you don't have food, you don't live. Simple as that. Your whole life in all four seasons revolves around food. In spring, everyone is out waterfowl hunting and egg-gathering. If you're lucky, you're plucking the first green shoots. This is the hungry season, because the salmon haven't started yet.
In May, the salmon start coming into southern Alaska. By June, they've made it up to Western and Northwestern Alaska. By July, every riverbank has drying racks filled with split-open fish. Dryfish is what keeps you alive year-round. If you're tired of salmon, you're tired of life. Seal oil is a preservative as well. You're stuffing salmon eggs and birds into sealskin bags of oil to preserve them and put them away.
Families are spread out across the countryside, and almost every major tributary has a fish camp of some kind. Only a few minders are left at the winter village.
August brings berry-picking season and silver salmon season. As October arrives, women are looking everywhere for roots and the last of the green things to be preserved. Nothing green is overlooked -- but mushrooms, for whatever reason, weren't used until modern times.
In the root-hunting effort, one favorite strategy is to follow mouse tracks and raid their burrows for roots. The proper move was to leave behind a dried fish or two in thanks.
By November, you're starting to settle in for winter. The shoulder seasons are the hazardous ones. You're into the rainy season, and travel is difficult. Drifting ice makes fishing difficult, if not impossible. Hopefully you've moved everything you need to your winter village, and everyone is settled in with full larders.
By December, you're in full-fledged winter. Girls and boys are fishing through holes in the ice. On the coast, men are venturing out to hunt polar bears. Inland, they're working to hunt caribou, herding them into enormous corrals where they will be slaughtered for food.
One of the constant tasks for women is the mending and creation of garments. In modern terms, a parka had the approximate value and importance of a car, but it was even more important. It, like food, meant survival. Seamstresses were in charge of preparing the skins and sewing them together. Women dressed not only hunters but their watercraft and sea otter charms. There were extensive spiritual connotations to this work as well.
To spice things up, there was midwinter trade and celebration. There was generally a trade gathering or festival in December or January, where groups could exchange gifts.
In general, women had a large role in trade and diplomacy, and as Jean Ray writes, women usually were the ones who negotiated fish camp sites and caribou hunting areas. This undoubtedly took place in winter, when many people were gathered close together, as summer dispersion made communication difficult.
What prevented these people going south to warmer climate?