Horses come in different types of colors. In order to be able to tame one you will need to be level 20. There are three types of horses : regular, sturdy and swift. Stables work the same as Animal Pens, but are for horses only. You will first have to find a foal, and then bring it back to a Stable to raise it. Getting a mount works the same way as getting a regular pet.
Mounts aren’t the only thing in Update 38, though: You will be able to engage in mounted combat and level up your pets and thralls, so they grow more powerful the more time you spend with them.