Okay, I find myself agreeing with Raven whole heartedly. My Grandfather trained cowhorses for 60 years to operate in and around the aggressive cattle once bred down here in Florida (brahmas and a type of longhorn called scrub cattle). The horses were trained to be smart, independent, avoid obstacles on their own, find their way home, stand still when the reins are dropped (no matter what noise ect.), and to not back down when the cattle got pushy (mine was down right aggressive right back).
Now I once had this arguement with a player so we went to a source: the guys who train the Lipperzaaners (Myakka, Florida has a ranch that breeds and trains these magnificant beasts). All those tricks you see Lipps do are based on cavalry horse moves. We were informed that the Lipps would defend fallen riders, attack nearby enemy horses (not of their own herd!) on their own, attack enemy infantry on their own ect. They would leap off the ground kicking out with all four hooves, hop forward on their hind legs and lash out with the front hooves, bite legs and arms, and yes, attack on command. The trainer was quite emphatic on that! These were uncut stallions and are aggressive all on their own to begin with (most reenactors use geldings for safety reasons!).
Yes, all this takes time. The horses must be bred for size (around 16 hands is average for a combination of speed and power), intelligence (contrary to popular myth dumb soldiers are bad soldiers) and for aggression (though not vicious, see former). Then they must be trained for at least two years, and then can only be ridden hard after a minmum of a year and a half after birth. Mind you we are talking only the horses of the knights: the elite of military society (think special forces in tanks). From my sources (the Royal Armoury Museum has some good sources) these would be only around 7 to 10% of the forces on any given side.
Mounted men at arms (decently armoured but non-noble cavalry) have much less well trained horseflesh. These are aggressive, uncut stallions and will charge, but are not trained to act on their own nor attack on their own. This being said though, they will go after strange horses and defend themselves of course. Some will defend a rider if they have a close relationship, though many riders could further train their horse on their time to do more. It's a cheap activity that takes up only a few hours a day (all you need is a guide rope and some open ground really).
This description could also refer to steppe ponies rode by bowmen who prefer to avoid mounted melee when they could. To note however, many mongols did train full fledged melee warhorses.
Now scouts breed for speed and intelligence, but were not expected to be combat animals and some sources say geldings were prefered fo stable temperment (much like many cow horses). Still they had a go-to-it attitude and avoided obstacles on their own and could follow voice commands.
Most PC characters not of noble background (or just rich as heck) will have at best the second variety (men at arms mounts). One can just by a high quality uncut stallion or gelding and do your own training. To make a decent cow horse took about six months of daily training and would be the equivelent of a scout horse (follow voice commands, not panic, charge, and not run off). Continued training is a matter of time and the requisite skills.
One last note. Based on measurements of skeletons, horse armour, saddles and desciptions given in contemporary texts the combat horse of the Middle Ages averaged 16 hands. The big 18 hand stallion was for jousting or parade. THAT is when a knight wore that tournament armour that turned him into a turtle and needed a horse of the appropriate size. In combat a knight not only wanted mass, he also wanted agility, speed, and a animal he could mount in a hurry (a knight was expected to mount in full armor of 60+ pounds, without stirrups and do it with a leap!). The jousters agree with this assessment. JUMPING on a HORSE in FULL ARMOUR! Gotta respect those guys! :shock: