Unlike other animal mobs, horses and donkeys are not following the player when holding golden apple or golden carrot.
This is Java Edition's problem.
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Can confirm for 1.17 pre-release 3
This is probably caused because for other animals, you use that item to breed them, not heal them. They are probably not coded to follow players with items used to heal them, only items to breed them.
Can confirm. Also affects 21w19a.