What do people in the North do when Winter cones around besides try and survive?

Great question! I can hazard a few guesses as to some areas of activity, based on cultures that have short(er) growing seasons and long winters. 

One would be handcrafts – Scandinavian farmers, for example, historically would often spend the winters building boats for sale to fishing villages (a practice known as beredskaparbete, which later gave its name to Sweden’s system of jobs for the unemployed) – so I wouldn’t be surprised if smallfolk in the North spent the long winter making new (or repairing old) farm equipment, housewares, clothing, and so on and so forth.

Another would be animal husbandry – European farmers in winter were advised to lop trees for fodder to help keep animals alive through the winter, for example, and in regions with lots of marginal land, animals would be herded from their normal fields to “preserved grass” land.

One that shows up a bunch in ASOIAF is story-telling: Old Nan’s “hearth tales” seem to be part of a practice of oral culture in the North that has preserved memories of the Old Night and similar ancient truths that the Maesters scoff at. While the North isn’t the only part of Westeros with a folk culture, I would imagine the tradition of story-telling is much deeper in the North than in other places, simply because they have so much time in the winters to gather together for warmth and while the time away.