there should be enchantable horse shoes that can make it go faster, jump higher and have frost Walker but another version like frost steed or something. Maybe also you can make iron ones but can only find diamond and gold ones
A horse as an extra item is a great idea. However, I believe enchantments should be added to horse armor as well if horse shoes get enchantments. The armor should receive protection enchantments whereas the horse shoe should receive agility enchantments.
That's is actually a great idea. I agree with putting the speed or frost enchantments on the shoes, 100%. The armor protects the horse it doesn't buff it and it just doesn't make sense to put and enchant that effects feet, on the body. And as far as protection enchants on the horse armor I don't think that is a great idea just because the horse is already protected by the armor and they have a good amount of health. Plus what do you run into that kills your horse.