Ixions

Horses are great but you know what would be even better than horses? Horses with stone skin and impenetrable scales like lizards, horses with giant eagle wings who cna fly, horses that are able to breathe fire or acid like dragons, horses that can run through rivers and breath underwater... hybrid superpower horses.
Ixions is a name for horse cross breed hybrids. There are very few stables that are actually trying to come up with a new breed of horses that would be able to rival anything else out there that is used for transportation. Some purely focus on improving the horse health and natural abilities, like their speed and their stamina and things like that, but there are horse handlers out there who want to create something new, something straight out of the walls of the old temples. 
Ixions are rare and so far unsustainable but with the help of magic and skill, these specialised horses are less of a rare sight than in the past. Some people think that it is not wise to try to tame the nature and make it do what you want and that experimenting with all of this only leads to creation of new dangerous monsters.
Others out there believe that if there are so many monster hybrids out there that can wreck chaos wherever they dwell, there must be some counterballance out there. There must be some equivalent of creatures that are basically a nice version of monsters and Ixions are the first example of that.
Most common hybrid horses are those that have only traces of other animals within them. There are horses that are able to sustain themselves in the dessert like camels can, there are horses that can see well during the night like bats can, there are horses that can leap better than any normal horses out there (wings help but they are still not enough to make them actually fly).
Don't ask horse handlers about centaurs though. That happened only one time in history, don't be weird about it, and it was actually a spell gone wrong, nothing more than that.