A horse can never become a zebra, although there are cases in which a horse and a zebra can mate and produce a hybrid offspring.

A horse does not turn into a zebra while horses & zebras are different species but they are related by the same shape & body structures.

When the horse goes to Ty Pennington of Extreme Makeover: Home Edition and says "Maaaayyyy wwwaaaant to baaaaeee zeeebraaa"

When he believes he is

They are separate but related. They are both among the Equine family.

When it gets the right paint job.