Glitchy Horses

Does anyone know of a trick to be able to use a zombie horse with barding (armor) on?

I want to re-texture and re-SFX this horse, and be able to use the barding as overlay layers still, but it seems to glitch out:



Same with skellies, mules and donkeys.

Is this just a missing texture- I mean can I add a texture to my resource pack with the correct name, and it'll just work?

Or are these armor/variant combinations just fundamentally unavailable client-side? I haven't been able to get it to show up, and sometimes it seems to (maybe?) go invisible and lock up the client in a bad way.

An alternate question- is there any way to spawn an invisible horse whose barding is visible?

And, yes, if you're curious- this is for broomsticks