This takes place in the Epic Mickey universe, in WastelandThe theater is actually the Mean Street Theater, which would explain why Oswald is coming from the "real world" instead of from inside the black-and-white cartoon. The black-and-white cartoon was claimed to be a "forgotten and recently unearthed" Mickey Mouse cartoon to prepare for the surprise of Mickey breaking through the screen, so it makes sense there'd be a copy of it in Wasteland. And we already know that in Wasteland, you can enter the projector screens and interact with the characters inside the cartoons, who eternally replay what there "original selves" were doing when the film was shot unless they are disturbed by an outside force. Thus, the characters who got out of the screen were not "really" the Mickey Mouse or the Pete, but magic copies of them at the point when they shot Get a horse !. Now the whole gang lives in Wasteland. it's gonna be a surprise for Mickey next time he visits Wasteland, to meet an exact copy of himself there !
WMG / Get a Horse!