Suggestion 1: All hats being obtainable on all sites
Kind of like what this answer suggests, however focusing on sites. My main focus is the lightbulb and hairboat hats. I was aiming to try and get every hat on Anime and Manga. However, to my knowledge, lightbulb is manually awarded by one of the SEx Gods (Stack Exchange Global Moderators) so even if I did get it chances are it would be here on Meta.
The hairboat hat on the other hand was obtained by posting a comment to a particular user and while this user is on Anime and Manga, they have no activity which mean the hat associated with commenting to them is unobtainable on Anime and Manga. Now sure, Anime and Manga is in beta, who cares? Well, there are also non-beta sites which would make it impossible for them to obtain (this is going just off from how many questions and answers this user has posted according to their Stack Exchange profile).
So if a hat is obtainable on one site, it should also be possible to obtain it on any site.
Suggestion 2: Being able to wear any hat after Winterbash
It's been suggested in an answer already, but my take would be to be able to wear any hat you have obtained in any previous Winterbash all the time. This can also lead to a more permanent Winterbash site where we can view previous years' hats we obtained (having wardrobe boxes for each year) and also the leaderboards from those years.
The hats then can also be used for other yearly events like April Fools (last year's for example, trading Hats for Bacon and trading Bacon for Unicoins).
Suggestion 3: Winner Hats
Who wants a hat from winning Winterbash and show it off all year (extending from Suggestion 2). We can have Winner hats for
- Network Wide Winners
- Local Site Winner
- Total Hat collected Network Wide
Obviously there would have to be a decision on whether network-wide winners can be eligible to also win the other winner hats and/or if winner hats can only be one once per person.
For example, being number one on Arqade and Science Fiction & Fantasy, if the user has more reputation points/time on Arqade they win the hat there and are no longer eligible to win it on Science Fiction & Fantasy?
In the example above, the next runner-up would take the winner hat and so on.
Suggestion 4: Complete Collection Hat
For completing the collection of hats for one site, sites can opt in to submit a design of their own (Metas get used to vote for the submitted design) and sites which don't opt in and young beta sites (if not all) have a generic one based off the favicon.ico used for the site.
If suggestion 3 is taken on board then hats from it and this suggestion do not count in the leaderboards (if suggestion 2 is taken on board a separate "wardrobe" would store "Special Hats").