When a horse that has a saddle or any kind of horse armor is affected by any kind of invisibility, the saddle and armor will not show. With pigs, the saddle does show, so I expected the same thing with horses. I don't know if this is intended but it seems like a bug to me. There can't really be any screenshots of it because you would not see anything.
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migrated
Unfixable. MC-13738
Jeb's comment:
Fixing this would create a whole bunch of special-case code, as the saddle and armor are baked into the horses' textures. After making a few stabs at the code, I decided it was not worth the effort / complexity. I will remember this when/if we add other mobs with armor in the future.