Horses are incredibly fragile, and over long distances would prefer to be moving at human walking speed.
Horses also require continuous grazing to sustain themselves, and because of how their digestive tracts work, really need time to amass energy.
It's not a question of "running down a horse." It's a question of heat exchange and endurance. Humans are incredibly efficient at maintaining homeostasis "under load." Horses are not.
If you read a histories any war/conflict where there are large numbers of horses involved, a common theme is them just dropping dead of exhaustion along the side of the trail, because they can't sustain the pace of the army marching with them.
>If you read a histories any war/conflict where there are large numbers of horses involved, a common theme is them just dropping dead of exhaustion along the side of the trail, because they can't sustain the pace of the army marching with them.
This is assuming that most of the army were full of people walking and the horses walking along side were getting exhausted? So an average human can walk down a horse?
But we can't actually run down a horse. Only top ultra marathoners can do that.
But walking down a horse? Really?