Zombie Horses spawning with horse armor

Zombies can spawn wearing all kinds of armor, from leather to diamond, so I don't see why zombie horses shouldn't be able to as well. It would be a rare occurrence and would serve to make fighting zombie horsemen more interesting as well as making horse armor renewable without making it craftable or easy to get. This also has the added bonus of making zombie horses easier to collect (as armored ones wouldn't burn and take less damage) while making the battle as a whole harder.