Depends on the period. Osmer will tell you a lot about the early Thoroughbred, which originally was a modern warhorse, with racing quite incidental, though in 17th-19th century horses speed on the battlefield was good. On the other hand, it's a little different in Xenophon's On Horsemanship and The Cavalry Commander c. 350 BC, for riders without saddles or stirrups. It's different again when the horses wear armour.

We first find evidence of domesticated horses at Sredni Stog, c.4000 BC, so breeding horses has gone on a long time. We find they spread from the steppes into Mesopotamia, which resulted in them being called "mountain asses" because the Egyptian domesticated donkey had preceded them as war animals, being used to pull chariots, as on the placque called "The Royal Standard of Ur."

Horses are preferred as war mounts, because they are generally larger, faster, and more sensitive to controls and training. They react to the rider faster, which can be critical. Also, stallions are fierce and combative, which is good. It's not just that they were rare status symbols. They were the high-tech weapon of their day.

Back in this heroic age, horses ran small. Spruytte (Early Harness Systems), built reproductions of various chariots, starting with an Egyptian survivor. The first thing he found out was that his horses were too tall, and he had to borrow a couple of ponies from a friend to suit the chariot. So if humans look a little large next to the horses in ancient art ... they were.

People were working on getting them larger. The breeding up in size took place on the steppe, where large numbers and still-wild populations gave them genetic variations to work with. Yes, they had the idea of breed yor two biggest animals to get big offspring. The tribes had commoners and a warrior nobility that was bigger than the commoners, in general.

As a result, just over the Zagros Mountains, the plains around the town of Nisa became famous for their really big horses. You can see them in the frieze of the Apadana Palace at Persepolis, c. 515 BC. (You can also see the dainty little Caspian horses that still survive.)

We first read about them in Herodotus. These were the wonder horses of the Persians who could outrun the Thessalian chariot-racing breeds, and were considered the epitome of equine beauty.

Now, I haven't mentioned training because that was the sort of trade secret passed down between illiterate horse masters. The one book we have is c. 1400 BC on how to get your chariot racing horses in shape. I gave what there is to a horsey friend from a horsey family, and our only conclusion is that the original text has become massively corrupted over centuries of copying and damage. It starts out well then gets senseless.

But we do know from Herodotus that the Nisaean horse of the Persian general, Mardonius, fought under him. There was even a special plan to kill the horse, it was considered so dangerous and frightening.

Now, if you look at the Parthenon frieze, you will see horses that are often described as "rearing." But they are not in a natural rear, like Trigger under Roy Rogers. They have their hocks bent well under them in a pose known at the Spanish Riding School of Vienna as the levade. Others may be leaving the ground in a courbette.

Together with Mardonius's mount, we can postulate that warhorse training was already advanced to haute école and the "airs above the ground."

Our first surviving books on horsemanship for war come from Xenophon, c. 350 BC. Much of his advice echoes the fragments of a lost author a generation earlier. Even though Xenophon was talking about guys on saddle blankets with no girth or stirrups to hold them on, he was the only author on the subject until the Renaissance. There are others who discuss veteranarian matters, or what's good conformation, but Xenophon was the last word in print for 1700 years.

Sort of.

(To be continued)

Sources:

Azzaroli, A.. An Early History of Horsemanship, E.J. Brill/W. Backhuys. S/b A History of Early Horsemanship.

Hyland, Ann Equus: The Horse in the Roman World (1990) Training the Roman Cavalry (1993) The Medieval Warhorse: From Byzantium to the Crusades (1994) The Warhorse: 1250–1600 (1998) The Horse in the Middle Ages (1999) The Horse in the Ancient World (2003)