Despite their entirely different names, player.cursor and horse.chest function exactly the same. You can set the chest of a donkey with player.cursor and detect the player's cursor item with horse.chest.

This also applies to player.crafting.(0-3) with horse.(0-3).

Steps to Reproduce

• Summon a donkey.
• Run the following command on it:

  /item replace entity (donkey's uuid) player.cursor with minecraft:chest

• Observe as a chest gets placed in the donkey's chest slot.
• Run the following command on it:

  /item replace entity (donkey's uuid) player.crafting.0 with minecraft:stone

• Open the donkey's inventory and observe that the first slot has been replaced with stone.

Code Analysis

Both player.cursor and horse.chest use slot id 499. Both player.crafting.(0-3) and horse.(0-14) start at slot id 500. Shifting the IDs of one set over should fix the issue.