Is there a official term for the people you'd find in theme parks dressed up in big furry 'cartoon character suits' like the Mickey Mice in DisneyLand?
The suits are called 'fursuits' and the actors/performers within them are, apparently, sometimes just called 'furries'. (There are web-pages devoted to the topic which you can find by doing a Google search. Mind you - as Jenny suggests - don't blame me for what the search throws up!)
I think there is some confusion here arising between people who as the questioner suggests dress up in theme parks or sports games for a living and the people who dress in aminal suits for sexual gratification (amongst many other reasons)....details on the latter can be found by searching for info on "plushies" or as QM suggests "furries" but this isn't really an adequate description of the first group....perhaps "Mascots" would come closest to what you are looking for?