I couldn't even find them with a jacket - had to go to sleeveless jacket... 
Don't know about huge at all since I don't have any chars that size...
Ok, I bet that was it. My huge had a jacket on (with short sleeves but it was out of the Jackets pulldown) so it must not be allowed. My female had a Baggy shirt on.
Santa gloves (once you get them through the Snaptooth/BNY mission) are under the Bare/Tight (or whatever its called) glove option, right? About halfway down the list?
A "huge" character of mine should have received them last night but can't find them (I have the badge as well so I know I selected it from the rewards). A female character of mine found them just fine so I know I'm not insane. Is there a problem with Huge models and them?
I even changed to short sleeves just in case there was a piece conflict making the Santa gloves not a valid option. Still no love. Boots work fine though.