So I recently went and saw The Revenant (awesome movie btw) and during the course of it I found myself wondering how these people could survive after doing things, such as primitive fishing techniques, that required them to be partially/fully in the water in freezing conditions. Another similar instance that I've been pondering is the fact that most of George Washington's Army was shoeless up to and including the Crossing of the Delaware River in the middle of winter!
Yes, I understand that it is a movie and all that entails, but I imagine that life went on regardless. As evidenced by the American Continental Army, people found ways to cope without suffering from frostbite, hypothermia, etc. So... how did they do this? Or did they all actually get frostbite and tons of people died from exposure/hypothermia?
I haven't had a chance to see The Revenant myself yet. However, frostbite happens much slower for relatively health people than you might expect. Even in some of the worst (dry) conditions imaginable, it can take an hour or more before serious permanent damage begins to set in on exposed skin. Wetness is to be avoided in all situations. The times national weather agencies list for frostbite are calibrated to the most vulnerable segments of the population for public safety and rather underestimate things for the vast majority of people. You would be unable to fish long before you got frostbite though, as fine motor functions are lost relatively quickly in my experience.
However, Native Americans would have generally avoided that situation in the first place with thick buffalo skins (such as this, windbreak shelters, fires, and intelligent behavior to avoid the worst weather. Even a thin layer of impermeable material and preventing heat loss from extremities can add significant time to injury. Stuffing boots and wrapping hands with hide are both well-documented behaviors in armies facing cold weather with limited resources.
So this does not directly address the circumstance you describe, but it gives you some ideas of how the natives adapted to harsh climates. This is an answer that I formerly provided in a related question here.
In my region, by digging holes. Beginning about 5,000 years ago, and continuing into the historic period, natives of the Northwest used semi-subterranean houses adjacent to large bodies of water to keep warm. The Columbia Plateau can get pretty cold. Native houses in that region were around a meter deep and had a wood superstructure and earth covering. Early on, ca. 5-6,000 BP, the houses were fairly small, about 5-7 m in diameter. Later they would get larger and elongated. Being at least partially under ground and the earth insulation raised the living area temperature significantly. Here is a cartoonish reconstruction. But you get the idea. House pits were used throughout North America during various periods of prehistory. They are pretty common. The definitive work on Native Plateau Architecture is Native American Dwellings and Attendant Structures of the Southern Plateau Harvey S. Rice, 1985. Eastern Washington Reports in Archaeology and History, Cheney.