Put the summary of the bug you're having here
I thought the horse armor would go on the horse no problem.
Instead the horse armor applied and gave me another set of armor.
Steps to Reproduce:
1. Get horse armor.
2. Apply to horse.
3. ...
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It's simply dropping the old armor and placing the new one on. But it shouldn't drop in Creative.
Did you do this in creative or survival? It's likely that if you're in creative, it's just creating doing its thing and not using up the item. The armour should then pop off the horse as well because you may want to change it.