As animuson himself said in his comment, the Winter Bash hunt is starting to feel "old" for many users. Reused hat triggers and hat pictures hurt one of principal interest trigger for the event: discovering new things.
As I have also said here, the "fun" in Winter Bash can be traced back to two central elements: competition and exploration. While the competition is still present - people compete to get more hats - it isn't sufficient to motivate some users that are less interested in climbing leaderboards. For this growing part of the community, the only interesting aspect of the event is finding new and funny things.
This can easily be "proven" too: notice how the knitting tool - something new and never seen before - got a lot of interest (some even started "post your best creations" questions) while the interest in hats somehow declined after it became evident that all secret hats were found.
Please, read my other answer I linked above for a more in-depth analysis of the situation.
So, it would seem easy to fix all this, right? All we need is something new and original, right? Well... it really depends on what our objective is.
There is an additional challenge that should be considered when trying to imagine Winter Bash: the cost/benefit balance.
As sad as it may seem, the primary purpose of the Bash isn't "FREE FUN & REP POINTS!". As the staff said multiple times, Winter Bash was made in order to try to fix another completely unrelated problem: decrease of users' contribution/traffic during the holiday period.
What does this mean? Simply put, that if we want to keep the original intent intact, any revision to the event should still be solving the same problem.
This is why we end up with reused hat triggers every year: the triggers were never meant to be just funny or original - they were crafted to promote some kind of behavior that the staff wanted to advertise. Voting stuff, posting answers, helping on the review queues - those are the things which are likely to earn you a hat, because those are the things that are likely to help the site traffic. Having a trigger for playing the Asteroid secret minigame on Arqade won't help anyone, and that is probably why my idea for an Asteroid hat is ignored every year (insert sad puppy face here).
It is unclear what animuson had in mind when he posted his reply. He did indeed state that he is bored with the current hat hunt, but he hasn't really made clear if he is actually proposing a full "for fun" event that completely puts aside the "promote traffic" requirement Winter Bash always had. Thus, I will only focus on the gaming aspect of the event, and will leave definition of the "behavior promotion" elements to others. I will also avoid considering costs/spending limits that the event will obviously have.
So, first of all - while hats are fun, they are getting old. Reused hats are the rule now, and therefore many more "casual" users are getting bored fast. Getting Identification Division once again? Trying to get another necromancer badge on your low traffic site?? SO BORING.
animuson said he would be interested in retiring hats. But retiring hats means we need another collectible thing, something that can also be displayed near your avatar.
I suggest we move to.... PETS.
While this doesn't really change much - in the end you are still winning a "picture", it should provide some "oooh, loook, new stuff" factor. Even better, combining the two aspects by giving users the ability to equip an hat and a pet at the same time could give enough distraction to keep things fresh and interesting for some time.
animuson also suggested moving to a "gacha / crane machine" approach. I kinda like this suggestion - removing the requirements to get an hat and switching to a "luck/minigame" approach means that we remove the "getting this hat is impossible for me" element that plagues Winter Bash: right now it is very possible that users are only interested in getting some hats that they like more - meaning that they will stop caring as soon as either they get the hat or realize it is almost impossible for them to do so. Moving to gacha rewards should help in both cases, by removing the reason to stop (why should you not play anymore if you can easily win coins by performing actions you would have done either way and maybe end up winning a new hat?).
Gacha has also another advantage that animuson didn't notice. Not only it decouples hats/pets from triggers, it also means that every single hat/pet can be secret. This in turn helps solving another problem: lack of new things to see. By giving each toy a different rarity, you can easily create a scenario that forces users into never being sure they have found every hat/pet.
Third, but I don't really want to go to much into this, decoupling the triggers from the actual unlockables means that the trigger may be more varied. You no longer need to just have a trigger that promotes good behavior, you may even throw in some random triggers for finding Easter Eggs and doing random stuff.
The "Why this won't be a thing"
While I personally would love a "collectible gacha pets" system... I doubt such a thing will realistically be made. While many of us would probably like it (even some staff members like Animuson) we have to remember something.
Time = Money = Cost
Winter Bash comes only once in a year. It only lasts a few weeks. And after that, all the work is thrown away in the trash (excluding some re-utilizable code base, that's it). It probably won't ever be worth puting too much effort into it, so while I wanted to post this idea since Animuson asked for something different, be aware that I am the first one that doesn't expect this to become an actual thing.
And one more thing...
I am adding this last chapter just to include a weird idea that I had while reading some kinda unrelated discussion in the Tavern chat room.
I think most Meta users know balpha. What they may not know is that some time ago he made a service that creates "random" unicorn pictures based on a string hash... He isn't the only one who had that idea: picture generation based on string hash is pretty common, usually used to generate avatars based on some user identifier.
For example consider RoboHash, which generates robots - or optionally cats - avatars based on an hash... or even something like CryptoKitties which provides blockchain based cat picture generation... and breeding.
Think you get what I am going for now?
Suppose we make some pet classes... let's keep thing simple for example... dogs, cats, unicorns and chickens. We then create 4 generators, one for each pet "type"... If you notice, given some artistic support, creating a generator is quite simple: compared to balpha's Unicornify service these generators are kinda "stupid" - they just combine some standard parts (eyes, tails, fur colors, body shapes etc) to generate a complete picture.
Now, let's return to our gacha game. Since we don't have complete pets anymore but just generators, our gacha machine will actually just provide random pets seeds that the generators will then translate to actual pictures.
The benefit? Now we have "infinite" pets, not just a set amount, only limited by the total number of possible combinations of the parts. Have enough parts and the chances of having a dupe will be very dim... In a single sweep we destroyed the biggest problem the event has - the "I have seen everything" problem.
It is also worth noticing that having "generated" pets doesn't mean you can't have "custom" pets too - all is needed is a special "custom type" category that utilizes a different generator. This could be easily turned in a "rare pet" category.
Since now pets have different rarities, we can also have different levels of "pets eggs". Back to animuson's example, we could have gacha machines that operates with 1, 5 or even 10 coins, each one with a different eggs rarity probability chart.
Also... pets generation creates space for another feature... Pet MIXING!
If you look at the CryptoKitties page, you will notice that they support "breeding". Since our pets are made up of parts, it is somehow "trivial" to mix two pets in a new one that shares parts from the two parents - for a cost, of course.
This feature solves two problems: first, it gives some use to pets we may not really like - mix them and hope the result is better. Second, we could somehow find a way to implement chat based pet mixing between users (still need to have a cost to prevent abuse) in order to promote Friendship (& therefore Magic).
Lastly, the gacha feature and generation brings us to one more opportunity that may become our doom... but could maybe somehow even actually work if we are not too greedy. Premium paid gacha roll. Meaning that if someone really wants to give a small real world coin to SE to thank them for all the work... maybe he could get a small three week little "look at me" pet out of it. Obviously this is just an idea, and I know many fear the day SE does "IN-APP PURCHASES"... but maybe it could work. Maybe.
(OK, I will be honest. I originally also planed for a way to have users being able to battle each other with their pocket sized pets... but it is probably better to save that for later)
PS: Shadow Wizard just made me notice that there is another option too - have the gacha machine give out pets parts and then have the users build their pets out of the parts they have unlocked so far. I like this option too, and maybe it could be simpler to implement while keeping all the advantages of my more complex one. The only thing we would lose is the option for pet mixing, but that hasn't necessarily to be a thing.
And YET another more thing (2019 update)
A random parrot in a random chat board just pointed out another interesting option: ugly sweaters.
I think that could work too - basic idea would be the same: sweaters could be procedural generated based on a random seed (similar to how gravatars are generated). They would still be bought with coins you would get from various task/trigger.
The fun part is that we could then implement a "gift an ugly sweater" feature to give out sweaters you own to other users. That would basically be the SE version of the old Christmas tradition of getting ugly sweaters as a present and then trying to get rid of them by recycling them as present for other relatives....
As an added bonus, the sweater could also list all its previous owners :P.