Questions about the origins/purpose of the hats have come up a few different ways in a few different places this year. I was planning on including a fairly detailed rundown at the end of the event. I think at one point I said in the blog post, although I've realized the post-mortem on meta would probably be better. I'll give a quick summary here, though.
Sufganiyot, A New Hope, The Airing of Grievances, O Tannenbaum, Auld Lang Syne
These are all for little more than showing up. Basically to let everyone get in on a few hats even if they're not super-hardcore about Winter Bash or even about Stack Exchange.
Every! Body! Gets! A Hat!, Specialist Hatsman, Fan-hat-ic
Hats about hats!? Mostly just for fun. I thought different communities might get into friendly competitions to see who would get Every! Body! Gets! A Hat! first. Specialist Hatsman is kind of a bonus for people who are really into Winter Bash. Fan-hat-ic is too, and it's a somewhat tongue-in-cheek nod to people who've complained that the Fanatic badge is too hard.
Cerro de Potosi, El Dorado, Hat Trick
All things that are existing rewards in the system, that we're just giving a bonus reward for.
No downvotes means you did a good job that day. Upvotes help limit the hat to people who were active.
be helpful and welcoming to new users with strong edits
Do You Even Lift?
Er, upvoted answers are good? Possibly the most self-explanatory "positive goal" of any hat this year.
Closing, reopening, deleting and undeleting are important parts of the SE ecosystem.
Encourage people to think of on-hold and closed questions as posts that need some extra love and improvement, not garbage to be hated and ignored.
Living in the Future
Look how much you've grown over the past at-least-a-few-days!
Get people good answers quickly. Probably ties with DYEL for most self-explanatory "positive goal."
Do it Yourself
Sharing your knowledge is a good thing, whether it's a tricky problem from your past or a case of "searched for half a day, couldn't figure it out, finally gave up and posted to SE, then realized the answer 15 minutes later."
On occasion, accepted answers are good but incomplete, become obsolete over time or are just plain wrong.
If you're looking for a hat to complain "there's no good reason!" about this year, this is probably your best bet. This one's pretty much just a shout-out to our mobile team.
Not all sites are programming-related. There's a use case in some of our heads where people will be in the garden or the kitchen and come across a problem but there's no computer handy. That's what the mobile app is for; load up Gardening SE or Seasoned Advice and bang out a question from where you are. In the field, as it were.
Breaking this up into categories made more sense at the beginning.
Old posts tend to get forgotten, but they don't always have perfect spelling/grammar/formatting/tags. Or answers, for that matter. They deserve sprucing up, and maybe the bump will even get some new/better info for them.
This one's also closer to the "just for fun" side. A reminder that we have an on-site search feature, because people (including us) joke so much that our real search feature is Google.
Vote Early, Vote Often
Same reason we have Suffrage, Vox Populi and Electorate. Voting is core to our system.
Giving authors of tumbleweed questions second chances at getting help.
Branch out! Try new things! Maybe there's a new site since last year that you don't know about but you're actually interested in!
This was carried along from previous years more from tradition than anything else. It's meant to be fun for the most hardcore hat fans but has probably outlived its time (or at the very least needs an implementation overhaul).
This belongs in the participation category above, it's just down here because it's a secret hat.
There's no positive behavior associated with this, it's purely an in-joke.
There are a lot of comments on the sites that live forever, which isn't the worst thing in the world, but doesn't match the original goal of comments. They were supposed to be lightweight, second-class content that stuck around just long enough to point out things that needed fixing/clarifying. This hat was supposed to motivate people to get rid of some of the obsolete cruft hanging around under old posts.
This serves the dual purposes of encouraging good close voting and increasing awareness of the dupe-hammer privilege.
It's Always 5 O'Clock Somewhere
This one's also just for fun.
We do a lot to encourage improvement, but not so much to reward existing awesomeness. Mostly because reputation increases already do that. This hat rewards awesomeness, though. A question that gets no comments was written clearly and completely on the first try. An answer that gets no comments can say the same, and reaching a score of seven proves that it's got good content as well. So the asker gets an awesome answer, and the answerer gets a cool hat (plus the usual reputation increase)!
It's Over 9000!
It's difficult to directly correlate views to quality, but there is a relationship there; generally speaking, more views tends to be better.
This served basically the same purpose as any "get upvotes" hat, plus it reminded people that anonymous feedback existed.
This was basically the highly successful Red Baron hat from last year, version 1.1. The benefit should be obvious; it attracts content so good that it improves posts around it.
There have been multiple requests for a Winter Bash hat for meta controversy. Here's one; here's another. I was especially supportive of the idea because I once proposed a badge for essentially the same thing. That proposal explains the benefit:
These criteria indicate problematic posts on normal SE sites, where votes are cast based on post quality. On Meta sites, though, votes indicate level of agreement, and such posts are generally suggestions that people are conflicted on. In practice, they tend to lead to good, insightful explanations of how the sites work or why certain changes should/shouldn't be made.
Many times, people don't answer questions that have already been answered, especially when the existing answers have already been upvoted. This is particularly true of bountied questions. But if you have something useful to contribute, you should go ahead and do it!
As far as positive behaviors go, this boils down to just writing a good meta post. The Grace Hopper/bug stuff, while important in other contexts, is just window dressing.