If it represents such a powerful 'tool', doesn't that disprove the hoodie theory? Or does Rayman just have a really badass hoodie?
The way I looked at it, In Rayman 3, Rayman replaced his neckerchief with a hood and just stuck it on top of his body in the same way as he did the neckerchief. I always thought that made sense, but then in Smash Bros for Wii U, Rayman's body had wrinkles as if it were a hoodie, which was pretty confusing, though it could just be an animator's error. Then Legends also has the 'naked Rayman' skin.
I also don't take the Rabbids costumes too seriously since it's not even confirmed if that's canon or not.