A normal horse mount

[Enkidoh]

Not a horse with a horn making it a unicorn.

Um, that's because it is a unicorn (the game outright identifies it as such!). This is a rather silly comment.

The lore of the game is that horses are not native to Eorzea at all, only unicorns are - the few horses found there were imported from the Far East (such as the Grand Company warhorses), or are magical constructs like Odin's steed Slepinir, as chocobos are the preferred mount for the more rocky terrain.

Besides, this is a Final Fantasy game, horses are usually rare in FF games anyway (chocobos are the usual replacement for transportation). They may introduce a plain saddleless horse mount in the future, as anything is possible, but it's unlikely.