I have two horses in a pen next to my base. One is wearing gold armor. The other I put leather horse armor, dyed red, on. I went to ride one of them today and noticed that the one I had put the leather armor on appeared to not be wearing any at all. So I checked its equip slots. The horse was still wearing the red-dyed leather armor. But instead of red, it was showing as white and thus blending into the horse (white horse with soot pattern).

I made a fresh set of leather horse armor, dyed it red, and equipped it to the horse. It still shows as white rather than red.