I guess all of us like fun. There's a long distance between totally serious and having fun like childs, which is also great. Somewhere on the way is the "hat game".
The moderators, including me, were a bit sceptical or neutral about this. I have the feeling that this activity may be great for the gaming site, maybe for cooking, fantasy and further sites in the whole SE network. A short mention in our chat did not really get much feedback.
Let's have a quick look at it from this point of view: we would like to attract further TeX experts. Does it help if the site is known as a TeX site where you once got funny hats as "achievements", for clicking vote buttons, posting questions or matching the christmas timeslot? Do we better outreach to people who still visit comp.text.tex and mailing lists, but not yet TeX.SE? I have some doubts. I know some experts who already don't like the reputation and badge achievement system, you can read an example in our current blog post.
To quickly see what we speak about, here's a screenshot I made right now from winterba.sh:
The site is great with its quality, and we have already much fun in the chat, in a personal non-automatized way.
Well, the hat game aka winter bash is going on at other sites. This is a very good opportunity to join also those sites and get some hats. Many are easy to get by simply voting or posting questions. Then we would know better how it feels with hats on. Learning from the feedback on other sites we can decide to join such an activity next year.