Cat Caps restore 3.3 Sanity/min while worn and are tier 1 warm clothing items, increasing the time a character can be without a fire during the Winter before Freezing. They have an insulation factor of 60.
Since Catcoons can easily go extinct on a map, and only drop their Cat Tails by chance, it is best to keep this Hat maintained with a Sewing Kit.
In Don't Starve Together, Skins can be applied to certain items to change their appearance. Information on how to obtain specific skins can be found on the Belongings page.
Woven - Distinguished Puppy Cap Not made of real puppies. See ingame
Distinguished Tied Trapper Hat This trapper hat appears to have been permanently tied up. Luckily it looks stylish that way. See ingame
Distinguished Trapper Hat This trapper hat is soft and cozy, but the ends don't seem to tie up anymore. See ingame
Since Catcoon is a portmanteau of "cat " and "raccoon", this item is most likely based on the real life Coonskin Cap, made most famous by the frontiersman Davy Crockett. Wickerbottom's quote references this by saying "Not quite like Crockett's, but it'll do."