The task for the Epiphany hat is to vote or post on January 6th (that is Epiphany, which is part of the Christmas holidays).
This is visible before clicking on the hat. The text you ask about is Italian, yet does not explain the task. It seems to be a reference to a song that I am given to understand somewhat fits the context. It roughly means "The Befana ...
Hats are not wanted here!
Like Emmy, we feel that being without a hat ought to be conserved!
Photograph of Emmy Noether copyright Universitäts-Archiv Göttingen; found in the Oberwolfach Photo Collection.
In preceding years per-site moderators were asked what their site wants. On this site, the moderators then launched a poll to base the decision on that result.
This year per-site moderators on sites that have a history of approving participation were not asked to begin with, and thus there was no trigger-event (or clear motivation) for a poll.
If it is ...
From Aarthi's answer on Meta Stack Exchange from a previous Winter Bash:
So, the official answer is: we over-awarded the hat so that people in Auckland / Tokyo / Shanghai / Vanuatu wouldn't have to wait until their midday to receive it.
This behavior will also occur for the other hats that are date-sensitive. This included L'Chaim, and will include Tis ...
So I guess you are talking about the Vote Early, Vote Often and Wireless hats, whose descriptions say, respectively
cast a total of 250 votes on any seven consecutive UTC days
vote on ten questions or answers using the Android or iOS app
One thing to keep in mind is that Community has not earned either of these hats on math.se, but on other sites. ...
Interesting. Most other hats are positioned on the page relative to user's avatar (position: relative), but this one is given absolute coordinates, with respect to the upper left corner of the page: (position: absolute). Presumably, said coordinates are calculated after the page loads and the hat-adding script can see where the avatar is. Trouble is, the ...
Description of Kofia hat says
first post between $12/26$ and $1/1$
As mentioned in this MetaSE post
It has to be the first post you did on a site. So if you've already left a question or answer on a site, you can't earn that hat for that site
If you still want to earn your hat you're welcome to make your first post on other SE sites.
This is not a bug as description of Naruto hat on Winter bash page says.
Post an accepted answer that receives no other votes for $12$ hours
And according to your reputation history and statement in question your answer was up-voted within few minutes.
The Community user has very many votes attached, see https://math.stackexchange.com/users/-1/community?tab=topactivity
A reason for this is that certain normal votes will be transferred to the Community user, mainly, to keep certain counts balanced in case of deletions.
Another, and perhaps more relevant to this, is that certain flags will cause an ...
You don't earn hats on Meta, and you usually also don't get hats for things you do on Meta, unless the hat specifically says "do X on meta". Quoting myself from Why didn't (or did) I or some other user get a hat although the requirements were (or weren't) fulfilled?,
Most hats are awarded for things you do on the main site, but there are a few* ...
The awarding of "hats" is a temporal activity carried out on the SE network around the change of the years, known as Winter Bash; by mid January all hats are gone. Very likely next December you can get new hats; the old stay still gone.
For the most part "hats" are like "badges," that is one gets them automatically (see note at the end, though) for some ...
It should be pointed that the recent top-bar altering scripts are incompatible with the hats button. If you are interested in hiding the hats, or following your progress you will have to disable it (for the time being).
Searchable leaderboard is available; however the search is by user name, not by hat name.
I don't think this is something we could realistically put in the data explorer. It would be a bit of a challenge because the event is very short-lived, and we'd have to do some interesting hackery to get the data into data explorer itself (creating the dump, dealing ...
As T. Bongers noted, one of the hats is actually three hats.
But if you don't have that one, you can still wear multiple hats. It only takes a little Photoshopping. You can even wear the same hat twice:
But with the built-in hat-adding script, you can't do these things. The script is buggy enough without multiple hat support.