Winterbash hats appear our profile when we asked a question, when we answered a question, in our profile page, but not our profile popup. Why? Is there any integration problem for this? If there isn't, please put this feature to the profile popup.
Sorry, I'm going to status-declined this just because: there's no good way to implement this right now without site performance taking a big hit.
That said, for myself, I rarely use that usercard popup (for one, despite moderator powers, I haven't earned it on many sites at all) so having hats there would be rather on the useless side for me. For another, it felt much more organic to change hats using the Winter Bash dropdown and clicking through my user profile. All other changes regarding my avatar happen by editing the email in my profile -- why not what hat I have equipped?
Your idea isn't bad -- we'll consider it for next year. :)