The Kencyr brought a special type of horse to Rathillien; the Whinno-hir—highly intelligent, extremely long-lived, and capable of great feats. It's not clear if the Kencyrath had any other kind of horse before Rathillien; they may have or may not, but three thousand years after their arrival they have many normal horses, as well as cross-breeds with the Whinno-hir to varying degrees, cross-breeds being the logical mixing between Whinno-hir and normal traits.
The Kencyr use the horse extensively in war, although, as in armies in our world, only a small proportion of their troops are mounted. All randon are trained in horsemanship.
When Jame comes across Arribek sen Tenzi's hunting party, he is mounted on a tall gray mare, and much of his hunting party is mounted as well. It seems likely that the hillmen of Skyrr are talented horsemen.
In the Southern Wastes, other mounts are generally preferred to horses (for example, fleetfoots, moas, woms) because horses are poorly equipped to the hot dry environment. However, one of the Waster Horde tribes is called the "Horse-head", suggesting that the Wasters keep horses.
↑Dark of the Moon, "Chapter 14: Gathering Forces" — "where the Silver narrowed slightly, ferries waited on either bank, linked by cables to huge winches. Powerful draft horses also waited in harness, swishing at flies, to set the winches in motion."
↑God Stalk, Book II: Crown of Nights, "Chapter 10: The Feast of Dead Gods" — "Meanwhile, another rider appeared on the rise, and another and another until the hollow was ringed with them. Jame, still watching the leopards warily as they circled her, began to feel very conspicuous. 'All right, all right,' said the first horseman suddenly,"
↑God Stalk, Book II: Crown of Nights, "Chapter 5: Winter Days" — "over the flagstones of the Res aB'tyrr's courtyard, circling the well, avoiding the mound of manure that Ghillie had just mucked out of the stable."
↑Dark of the Moon, "Chapter 15: The Killing Ground" — " 'He says the Horse-head and the Goat-eye tribes have, as well as several others.' "