The bug

MC-110903 was fixed in 20w46 snapshot and resolved the issue of replacing a saddle with air for horses.

The issue does however still remain for donkeys/mules/skeleton horses/zombie horses. The saddle can't be manipulated at all for these entities using the item command.

For all of these entities the player can manually add/remove saddles from them.

How to reproduce

1. Summon a donkey/mule:/skeleton horse/zombie horse

   /summon donkey ~ ~ ~ {Tame:1}
   /summon mule ~ ~ ~ {Tame:1}
   /summon skeleton_horse ~ ~ ~ {Tame:1}
   /summon zombie_horse ~ ~ ~ {Tame:1}
   

1. Try to Add a saddle:

   /item entity @e[type=donkey,limit=1] horse.saddle replace saddle
   /item entity @e[type=mule,limit=1] horse.saddle replace saddle
   /item entity @e[type=skeleton_horse,limit=1] horse.saddle replace saddle
   /item entity @e[type=zombie_horse,limit=1] horse.saddle replace saddle
   

   →  See "No targets accepted item [Saddle] into slot 400"

1. Try to remove the saddle:

   /item entity @e[type=donkey,limit=1] horse.saddle replace air
   /item entity @e[type=mule,limit=1] horse.saddle replace air
   /item entity @e[type=skeleton_horse,limit=1] horse.saddle replace air
   /item entity @e[type=zombie_horse,limit=1] horse.saddle replace air
   

   →  See "No targets accepted item [Air] into slot 400"

Expected Result

Was expecting this to behave the same way as it does for horses.

1. Summon a horse

   /summon horse ~ ~ ~ {Tame:1}
   

1. Try to Add a saddle:

   /item entity @e[type=horse,limit=1] horse.saddle replace saddle
   

   →  See "Replaced a slot on Horse with [Saddle]"

1. Try to remove the saddle:

   /item entity @e[type=horse,limit=1] horse.saddle replace air
   

   →  See "Replaced a slot on Horse with [Air]"