What is the objective behind "hats" ? I mean, apart from celebrating, will it reflect in your profile even after the winter bash ? (i. e. 4th Jan 13) ? your thoughts ?
From the Winter Bash website
"Stack Exchange invites you to celebrate the end of a great year ...with HATS! As you use your site, you'll discover hats and other items hidden behind certain actions. Collect all of them, some of them, or none of them, but be quick – the hats get put back in their boxes on January 4th!"
So most likely the idea behind them (besides fun) is to promote certain actions. A concept fairly similar to the usual badges, just a bit more seasonal/playful.
And no, after January 4th 2013 they will no longer remain. It will be a sad day for hats.