I had previously been under the impression that skins carry over between characters, but while playing the slots with my other character I realized that all the "[Vendor] customer service" skins were all able to be used again. I'm positive that my main character already had these unlocked.
Which skins (if any) carry between characters? I got in on the Halloween skins and since we can only get one for each character, I'd hate to waste it on a character if it won't carry over.