No, the stripes are not painted on. This is called a 'zorse'. A cross between a zebra and a horse. Similar to a mule, which is a cross between a donkey and a horse.
Isn't it cute?!? This is a zonkey, a donkey and a zebra cross.
Similarly to mules and other hybrid animals, zorse's are sterile. Because of the mis-matching chromosome's each animal carries, the resulting baby cannot reproduce. Pretty interesting, huh? I think there may be a few rare cases in which a mule can reproduce, but don't quote me on that.