That they insisted on making cats, horses and bears by making them cultures seems rather silly to me. All the health, stats and fertility is done with a trait that can't be randomly generated or inherited already, and the portrait rendering system can easily override portraits for characters with a certain trait. Either the hardcoded "Mohammed" method, or just by using the prisoner overlay like many mods already do to add disease, eyepatches or ugly overlays.

Better to do that, then it doesn't matter if you manage to make your horse a bishop, or somehow manage to breed him, because the resulting characters will just be normal humans of whatever culture the ruler who spawned the horse had.