Actually the two are very different. The only similarities is that they look somewhat similar (in the same way a wolf may look like a dog) and that they share a common evolutionary ancestor.
Male Zebra have fighting fangs (yep, you read that right). They are extremely aggresive and are quite adept at biting (a zebra that is trying to fight off other males so it can mate, or one that is fending off a predator, does much more than a horse does ....much more than flashing hooves and neighing ....think flashing hooves and slashing teeth). While such tactics are nothing to a lion they can give a person sufficient body alteration to spawn instant conversations at a thousand Christmas parties and bar outings.
There was a movie called 'Sheena: Queen of the Jungle' (your typical 1980's b-flick about some Tarzan-esque woman who can speak to animals and all that jazz), and in it Sheena was riding a Zebra. Well, it was actually a painted horse. They tried Zebra, but they quickly discovered it was far more prudent to take the time to paint a horse rather than risking losing the arm of their leading lady.
Comparing a zebra and a horse is like comparing a highschool amateur wrestler with a Ukranian combat Sambo master ....they are both grapplers, but they are also several light years apart.
Am I saying Zebra cannot be tamed? No! Any animal can be 'tamed' to some extent. It is just that the comparative risks between taming even the wildest stallion (and there are risks, especially when a fool and a wild horse come together) versus trying to tame your standard Zebra (PARTICULARLY the males) is quite substantial. A bucking bronco and a biting zebra are at two very different pay grades.
"Am I saying Zebra cannot be tamed? No! Any animal can be 'tamed' to some extent. It is just that the comparative risks between taming even the wildest stallion (and there are risks, especially when a fool and a wild horse come together) versus trying to tame your standard Zebra (PARTICULARLY the males) is quite substantial. A bucking bronco and a biting zebra are at two very different pay grades."
It is true that the zebra and a wild horse have different temperments that may affect domestication. However, keep in mind that the current wild horse was derived from domesticated horses brought over from Europe and escaped. There were no horses in north America at the time of Columbus. The ancestral wild horses may have had temperments closer to the Zebra. I agree it would be very difficult to tame/domesticate full grown wild zebras. It would be much easier to start with captured young or orphaned zebra and raise them away from the herd. You then select for mild temperment over many generations. Theoretically it should be possible to domesticate virtually any wild animal you can get to breed in captivity. Of course some would be more difficult than others and the price of failure more severe with a tiger than a cow. Maybe that's why we drink cow's milk instead of tiger milk.