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.

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    They probably did not want any math hatter jokes. – Toon Krijthe Jan 3 '13 at 13:53

Hats are not compulsory.

Some sites didn't sign up to have hats.

Even if a site did sign up you can opt out.

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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.

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