Wearing another bear's costume
You can wear the costume of any bear you've recruited to your village. To do so, tap the bear then tap the Wear Outfit button. Note that this is (as of the time this article was written) purely decorative; there's no advantage to wearing a costume.
To switch to a different costume
Tap the bear wearing the costume you want, then tap the Wear Outfit button. You'll switch right to it. (You don't have to take off the current costume first.)
To remove a costume
Tap the bear wearing the costume you're currently wearing, then tap the Remove Outfit button. You'll go back to not wearing a costume.