Hmm... Well, the new Thundercats assumes that everything takes place on one planet. Theoretically, Equestria could exist somewhere on Third Earth, especially with all the intelligent animals or animal-human hybrid types.
But... Where the Thundercats are is only one possible continent in one hemisphere. Go around the world to the other hemisphere, and you have a set of two connected continents that the natives of which call the world "Eternia."
Bambi can come from everywhere. Maybe Fluttershy encouraged him to seek out his dreams in Canterlot.
And thus the ultimate fan fiction was born...once the Care Bears find their way to Ponyville and the Cybertronians discover this Third Equestria's existence. Oooh, and the Ninja Turtles and Ghostbusters somehow end up in a wormhole caused by the Technodrome going haywire because it tried to use the energy of Gozer.