I'm talking about snow storms that occur maybe only every hundred years or so and drop feet of snow over a relatively short period of time. I'd imagine some tribes were more accustomed to large snows than others, but what about tribes that lived in areas that weren't? How would they survive this? I would think gathering any type of food with maybe the exception of wild game would be close to impossible. Did they have the food reserves to survive weeks? Simply traveling in feet of snow would be exhausting without proper footwear. The snow would probably last for quite sometime, assuming the temperature stays even relatively cold. Would snow of this caliber have been devastating or simply a mild inconvenience?
This doesn't exactly answer your question, but the Popular Questions page in the sidebar has a section on How did earlier civilisations deal with hurricanes and tornadoes?. It's not exactly how they dealt with snow, but there may be some similarities you'd be interested in reading about.
EDIT: And if you do a search for something like "blizzard" you can find previous questions like How did Native Americans handle harsh winter weather such as blizzards? Did they have any way of predicting foul weather? that might answer your question.
As for transportation, there are a huge number of snow-shoe designs indigenous to North America, particularly the northern Great Plains.
As for food, pemmican is a type of food made from dried meats, animal fat, nuts, and berries that could be stored as bricks wrapped in animal hides for extended periods. It is a high energy food and often used by Plains/Great Basin Groups.
I'm not sure about extremely harsh (but infrequent) blizzards, but most Plains groups did continue hunting during winter months, partly with the help of the aforementioned snow shoes and pemmican.
As for agricultural societies, like in the US Southwest (where blizzards are quite infrequent, but do occur) and along the Mississippi and east coast, most agricultural societies store large quantities of food just generally to help buffer against bad years. For instance, Pueblo groups on the Rio Grande were known historically to store between 2 to 3 years worth of corn as a fail safe for bad harvests/low rainfall. Of course, these stores could be tapped into for exceptionally harsh winter weather as well.