That said, since I can’t resist responding to random comments: are horses really being bred for sprinting as fast as they can for 20-30 seconds? (Isn’t that what cheetahs are so good at?) What is the military/agricultural/trade context in which that is relevant? Who cares other than horse racers? Over any of the distances where people are using horses I would expect them to be considerably faster than cheetahs even if both are unburdened. I don’t know much about horses though.
My understanding is that the primary military use of horses in Europe for elites was charges into massed infantry, which were not all that much longer than 30 seconds (rarely more than a few minutes). I would expect them to care more about things like carrying capacity and psychology than sprinting speed (as you want to stay in formation, and be able to break thru even if they don’t break formation). Other places focused on horse archers, which involved the horses moving rapidly for much longer periods of time, or skirmishers, where you cared more about the cheetah-like ability to run down someone trying to get away from you.
My understanding is that the primary military use of horses in Europe for elites was charges into massed infantry, which were not all that much longer than 30 seconds (rarely more than a few minutes). I would expect them to care more about things like carrying capacity and psychology than sprinting speed (as you want to stay in formation, and be able to break thru even if they don’t break formation). Other places focused on horse archers, which involved the horses moving rapidly for much longer periods of time, or skirmishers, where you cared more about the cheetah-like ability to run down someone trying to get away from you.