I could be mistaken, but I'm remembering something from the New Year's event where it was said that horses were utterly forbidden in the Twelveswood. Like... expect instant Greenwrath if you bring a horse in, the context seemed that strong. Whether or not it would actually happen or if it was a long-running rumor the chocobo breeders propagate to keep their monopoly is open for debate.
I could be wrong on remembering that, though, and I dunno if event stuff is always considered canon.
I could be wrong on remembering that, though, and I dunno if event stuff is always considered canon.