Nobody ever lost his life in battle from the bite or kick of a horse. It is men who do what is done in battles.

-- Xenophon, Anabasis 3.2.18

I'm not sure where you picked up the notion that horses have been described as lethal weapons throughout history. Xenophon, an Athenian soldier/philosopher/historian who lived c. 430-355 BC, is one of the oldest surviving experts on horses, horsemanship and cavalry tactics, and his view on the matter is clear from the passage above. Xenophon wrote an entire treatise on horsemanship and fighting on horseback - you can read it here - but never once says anything about the horse as a fighter.

This is not to say there weren't exceptions, including one famous example from the 490s BC, recorded by Herodotos:

Now the horse which Artybios rode was trained to fight with infantrymen by rearing up. Hearing this, Onesilos said to his attendant, a Karian of great renown in war and a valiant man, "I learn that Artybios' horse rears up and kicks and bites to death whomever he encounters. In light of this, decide and tell me straight away which you will watch and strike down: Artybios himself, or his horse." (...)

As for the two generals, Artybios rode against Onesilos, who, as he had agreed with his attendant, dealt Artybios a blow as he bore down upon him. When the horse struck his hooves on Onesilos' shield, the Karian cut off the horse's legs with a stroke of his curved sword.

-- Hdt. 5.111-112

It seems at first glance that this is exactly what you're talking about, but the only reason Herodotos would find this story worth retelling is because it was so unusual. Horses weren't normally trained to fight, and this particular horse was a famous exception; its opponents had to take special precautions to defeat it.

Most horses would not have been this aggressive, and their riders would mostly have tried to keep them out of range of edged weapons. Mounted combat in Ancient Greece could go to the lance or sword, but more commonly, cavalry fought at range with bows and javelins until the enemy ran away. It was only against a routing and defenceless enemy that they would press their advantage and get stuck in.

As Xenophon's treatise will tell you, the horses of the time were not large, nor were warhorses selected for size. Agility, durability and good character (willing obedience) were prioritised. Most cavalry mounts of history are much smaller than we think, and certainly smaller than the average horse today. Archaeological evidence shows that the average Greek horse (undifferentiated by role) stood about 130-140cm at the shoulder. Even breeds that were famous in Antiquity for their use as military mounts, like the Nisaean (from Parthia), were no bigger.

They were also unshod. Indeed, most of the trappings of modern horseback riding postdate Classical Antiquity. Greek cavalry rode without stirrups or saddle. Persian and Macedonian cavalry was the same. (It is often argued that this was the reason for their skirmishing tactics, but this is clearly false, as many Greek and Persian horsemen did charge into battle with lances, and did so with enough force that their lances often broke on contact.)

Xenophon should provide you with all you want to know about how Greek warhorses were selected. His treatise covers in great detail what physical traits and spirit a good horse should have, and how it should be trained for service in war. There are also some great general studies in modern scholarship if you'd like to know more:

• J.K. Anderson, Ancient Greek Horsemanship (1961)

• P. Sidnell, Warhorse: Cavalry in Ancient Warfare (2006)

• A. Blaineau, Le Cheval de Guerre en Grèce Ancienne (2015)

• C. Willekes, The Horse in the Ancient World (2016)

1/2

I’m going to take this opportunity to expand on /u/Iphikrates, answer, which is 100% accurate, as we would expect from them. There is really only a small window in the history of the military horse, where such training would even be plausible, for reasons u/Iphikrates, touched on. From the genesis of mounted warriors (and even before, in the chariot age), there were three basic types of horse soldier; light missile armed, heavy shock, and mounted infantry. As u/Iphikrates said, for the first thousand years, give or take a century, light cavalry were overwhelmingly favored. Before the invention of the Roman four horned saddle, shock tactics were difficult against massed infantry. Lances were normally wielded two handed in this period, as a stabbing weapon, not couched under the armpit, and you could not very well expect good results riding bareback into a disciplined Macedonian phalanx, wielding 15 foot long sarissa. The bareback seat was not stable enough for such tactics, and it would be difficult to even get horses to do it. Shock cavalry tactics were not decisive in the ancient world. Light cavalry played a much more important role, and was the centerpiece of numerous ancient military systems, such as the Scythian and Parthian empires. These missile armed troops (javelins, bows and slings), performed hit and run attacks on massed infantry, charging, releasing a barrage of missiles as they wheeled away in formation, then regrouping and rearming. These attacks whittled away at the combat effectiveness of infantry, demoralized them, and tied them down so they could not maneuver or communicate effectively. Heavy cavalry did have a role. Nothing was better for exploitation. If an enemy formation broke, heavy cavalry could swiftly pour through the breach, running down fleeing soldiers, destroying command posts, and generally wreaking havoc. Their mobility also made them useful for flanking attacks, where they were less likely to face massed, disciplined, spearmen or bowmen.

Although the Roman saddle greatly increased the combat capability of heavy cavalry against infantry, it did not really become a decisive arm in European warfare until the Medieval era. What changed to make heavy cavalry so effective? Essentially, it was a product of the de-professionalization of armies. The Romans practiced combined arms warfare. We think of them as heavy infantry centric, but in reality, every legion had attached light and heavy cavalry, artillery, and organic engineering components. This served them incredibly well as they expanded into empire. But when the Western empire decentralized, the ability to raise and train professional armies eroded.

By the 11th century, at say the Battle of Hastings, we see armies of nobles and farmers, cobbled together on short notice, with no coordinated training at all. Men at arms were often exceptional individual fighters, who trained very hard at individual combat. But there was no way to teach them formation tactics, much less to teach their retainers and other assorted support troops advanced infantry tactics. This was an enormous advantage to heavy cavalry. Without disciplined, trained, and appropriately armed infantry formations opposing them, shock tactics became decisive. So in this period we see increasingly heavy and specialized cavalry, serving as the focal point of the battle. With that came a whole cult of the individual mounted warrior, with its own mythology, hierarchy, and specialization. Men at arms, and especially knights, were locus of military power. Well, sort of. In reality, the locus of military power was fortifications and siege. And that may sound counterintuitive, because cavalry are useless in siege. But, if you want to take a castle, you need an army, and to have an army you need to be able to raid, which is how armies were paid in that era, and destroy raiders, which is how you kept your wealth. If there was a set battle, it was often the result of a raid and counter, like Crecy. Under these conditions, we begin to see where the horse itself might be used as a weapon, in a melee with disorganized infantry.

As u/Iphikrates mentioned, there was another medieval development that plays a potential role in your scenario: shoes. Today, we think of shoes as ubiquitous and necessary. But even after their invention, horses outside of Europe continued to work and fight under a wide variety of conditions, barefoot. Why did the European develop shoes, and why were the Mongols able to fight them just as effectively barefoot? Well, in addition to the rise of heavy cavalry, Medieval Europe also saw the preeminence of permanent fortifications. War horses, and increasingly horses in general, moved inside the castle walls, where they lived in stalls, with diminished freedom of movement. Horses evolved to constantly move. Their foraging habits, digestive system, and hoof structure rely on constant motion. When stalling became the norm, digestive and hoof problems radically increased. A horse standing in its own waste all day, rather than wandering over varied terrain, will start to lose hoof integrity. Walking trims the hoof, toughens it, increases blood flow, and allows the horse to self treat inflammation by standing in cold streams (which mustangs will do in the spring when they are at risk of laminitis). Our old friend Xenophon had something to say about this too. While the Greeks did not stable to the extent our knightly friends would, and had a more amenable climate for it, he describes both the problem and the remedy,

“But if food and exercise with a view to strengthening the horse's body are matters of prime consideration, no less important is it to pay attention to the feet. A stable with a damp and smooth floor will spoil the best hoof which nature can give. (7) To prevent the floor being damp, it should be sloped with channels; and to avoid smoothness, paved with cobble stones sunk side by side in the ground and similar in size to the horse's hoofs. (8) A stable floor of this sort is calculated to strengthen the horse's feet by the mere pressure on the part in standing. In the next place it will be the groom's business to lead out the horse somewhere to comb and curry him; and after his morning's feed to unhalter him from the manger, (9) so that he may come to his evening meal with greater relish. To secure the best type of stable-yard, and with a view to strengthening the horse's feet, I would suggest to take and throw down loosely (10) four or five waggon loads of pebbles, each as large as can be grasped in the hand, and about a pound in weight; the whole to be fenced round with a skirting of iron to prevent scattering. The mere standing on these will come to precisely the same thing as if for a certain portion of the day the horse were, off and on, stepping along a stony road; whilst being curried or when fidgeted by flies he will be forced to use his hoofs just as much as if he were walking. Nor is it the hoofs merely, but a surface so strewn with stones will tend to harden the frog of the foot also.”

(contd. below)