The Bug:

Horse armor and carpets cannot be equipped onto horses or llamas by right-clicking them whilst having these items held in your hand.

It's an intentional feature that saddles can be equipped onto horses by right-clicking them whilst having this item held in your hand as stated in MC-183073, so it would make sense for this same idea to work with horse armor and carpets.

Steps to Reproduce:

• Obtain some horse armor and any kind of carpet.
• Summon both a tamed horse and llama.

• /summon minecraft:horse ~ ~ ~ {Tame:1b}
  /summon minecraft:llama ~ ~ ~ {Tame:1b}

• Attempt to equip the horse with some horse armor by right-clicking it whilst having the horse armor held in your hand.
• Attempt to equip the llama with a carpet by right-clicking it whilst having the carpet held in your hand.
• As you attempt to perform both of these actions, watch closely.
• Take note as to whether or not horse armor and carpets can be equipped onto horses or llamas by right-clicking them whilst having these items held in your hand.

Observed Behavior:

Horse armor and carpets cannot be equipped onto horses or llamas by right-clicking them whilst having these items held in your hand.

Expected Behavior:

Horse armor and carpets would be able to be equipped onto horses or llamas by right-clicking them whilst having these items held in your hand.