Some users in many sites wear hats. But it seems in some other sites like Math.SE there to be no hat. So I'm curious about why.
Hats are not compulsory.
Some sites didn't sign up to have hats.
Even if a site did sign up you can opt out.
Some sites opted out of the Winterbash, and noone earned hats on such sites.
You'll have to ask the moderators of Math.SE themselves for their reasoning.