Anyone who breeds a zebra to a horse or breeds their horse to a zebra is, in my book, just another backyard breeder. They are breeding for color and the "wow" factor, not for conformation or to improve a breed.
Zebras are wild, dangerous animals. I have seen videos of people barely being able to ride a zebra to people putzing around on one without a care.
We have plenty enough unwanted domestic horses already. Why someone would want to bring another species in to add to that number, I'll never know.
However, I DID catch myself looking up "Dressage Zebra" the other day on google ;) I got curious. Not sure I agree with attemting to ride a wild creature (because if a professional does it, you bet your backyard horseman will try), but I was curious.
Also, I'm not quite sure if the same vaccines you'd use for a horse would work on a zebra? Does anyone know? And what are the regulations for sending a zebra to auction or slaughter if you don't want it or can't keep it anymore?
Before I went to school, someone had the opportunity to buy a zebra from a zoo and wanted to know if the could bring it. The facility said no, only horses. I can see their point of view.