I catch up on everything I meant to do during the summer and didn't have time for. Depending on how I'm playing, in the first winter, that might mean getting enough money for fruit trees, or mining/ buying enough stones for staircases, or maxing out fishing so I can get all the legendary fish the following year.
Year 2 is getting to the island, running the volcano enough to forge everything, running Mr. Qi's tasks to buy recipes and ease-of-life items, and making sure I have everything in place for Grandpa's evaluation (which is when the game was intended to do it's original scoring).
If I'm being really aggressive, I'll try for Perfection by the end of year two. I never make it, though, I'm just not interested in getting married and having kids :( but I go for my own (no- family) perfection anyway.