Outfits are vanity items that can be unlocked by collecting mystery boxes. Once an outfit is unlocked, it can be put on the character it belongs to in the treehouse building. There are 39 outfits in total, four for every character except for the Horse which has three. Each outfit also comes with a host of different colors.
"So if you weren't satisfied with a horse wearing a red bow tie, green is now an option." - Kyler Kelly-tan, game devcharacters have four outfit slots, others have three slots with two different outfits in one of them.
Most outfits are clothes or other vanity items but it's worth noting that each character has one "alternate skin" outfit that changes their overall appearance, often to that of a different species of animal. Here is a list of all the skins: