Going back to Budiansky again, he suggests that people initially started keeping foals as pets, sometimes no doubt having killed their parents for meat, so familiarity with horses and appreciation of their uses may have built from there.
I think that idea is quite likely from what we know about the propensity for all kinds of human societies to keep pets, taking in sick or orphaned animals to live with them, even from species that they usually hunt or farm. For example, various peoples in the Amazon keep a wide range of animals as pets, from tapirs to monkeys to parrots, often not for any particular utilitarian reason, merely for the pleasure of having the animal around.