Zombie Horse armor will go into the equipment slot but is not visible and has no effect to protect against the sun (they still burn up). I have only tested this while using the RealismCraft addon.
MCPE-233288
Zombie horse armor invisible and has no protection from the sun
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The horse armor appearing invisible is an issue with the RealismCraft pack. You will need to report this issue to the pack creator.
I am not able to reproduce the zombie horse burning. Please attach a video showing this issue.