It is possible to enchant the horse armours via the anvil, however it is not possible through an enchantment table.
When this enchanted armour is equipped to the horse in creative, you receive another diamond armour in return but the enchants are not equipped. While in survival, when these enchanted armours are equipped to the horse, the enchants are lost.
Horse armor enchantments have not yet been implemented, but you can always enchant any item in creavite. Duplicate of MC-4753.