When you are riding a tamed horse, if you use a sword on it, its durability wears down and the horse suffers no damage. I assume that you're not supposed to be able to hit your horse as you ride it.
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migrated
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Confirmed.
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Duplicate of MC-4732.
AgentM
note: the horse will not take damage if you try hitting it with a sword but de sword does get damaged!!!
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MC-4732: Tools and weapons lose durability without doing damage
Confirmed, you can test this by riding a horse and hitting it with a gold sword, the sword will lose durability when the horse is hit.