Can anyone please explain these hats? What if someone has all the hats? Is there an improvement in someone's profile or something else?
There are no new badges, only hats (and masks) and they are temporary:
What happens after January 4th?
After January 4th, the sites go back to normal and all hats disappear. This is meant to be a fun end-of-year celebration, not a permanent addition to the site.
What if someone has all the badges? Is there an improvement in someone's profile or something else?
That someone will then probably win Winter Bash, but there's nothing permanent here either, except that the winners of Winter Bash will probably be mentioned in the closing blog post. The leaderboards will be gone too (except that you can probably find copies in the Wayback Machine).