What do I do with these ridiculous hats. And my grammar may be wrong because I am a foreigner. Posting here is not easy - too many stupid rules.
They are hats.
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!
Unofficially? Well, they're fun cosmetic addons for your avatar that you get awarded for doing stuff around the sites.
If you don't want a hat, click on the snowflake and pick "I hate hats" and its gone.
Its a little like a festive, transient badge, and if it dosen't interest you you can just ignore it