This is the first year that I pay attention to hats (I love hats!) and I wonder if I will keep my hats for next year?
Or will I start over with zero hats next year?
No, we don't keep our hats. Hats go back in the box when the Winterbash is over and they don't come out again. None of us who played last year kept any hats.
From the FAQ:
What happens after January 3rd?
After January 3rd, the sites go back to normal and all hats disappear. This is meant to be a fun end-of-year celebration, not a permanent addition to the site.
It's only fair to you newcomers we didn't. :-)
You'll start with zero hats next year...in addition to it not being fair to newcomers if some users have a two-year head start, we change the hats (the illustrations, names, and triggers for awarding them) from year to year. The hats you can earn this year won't be available next year.