For some time there have been murmurs saying “Hydaelyn is a world where no horse exists,” but this isn’t the case at all. We actually created the whole world view with the vision that horses and their subspecies inhabit (or used to inhabit) the world.
For example, one of the four High Houses of Ishgard, the House of Fortemps, features a red unicorn on a black background for their crest’s motif. This unicorn is one kind of horse species. Shields that NPCs have equipped also have unique drawings on them, so if you are interested, try hunting those down.
Also, Odin, which we introduced in the 2.0 documents, is also riding his famous steed. While I can’t get into too much detail, we have laid down the proper foundation for Odin’s companion.
So while it may seem like there are no living horses in the currently accessible areas of Eorzea, there are in fact horses when you consider the entire planet of Hydaelyn.
Hyur and Lalafell travelled to Eorzea long ago and it is because their ancestors utilized horses as mounts that you can see remnants of this in their speech and crests.
So… why aren’t horses imported in modern day Eorzea? The reason is that trustworthy chocobos, that are better suited for the weather and environment of Eorzea, exist.