Docking is a hideous thing to do to any animal. Usually, it involves removing the tail, although, some also hack off ears. If not done properly (if that can be used here to describe such a disgusting thing) the animal can further suffer, not only the pain of the docking, but also, rectal prolapse.
Docking horse's tails was banned in the UK in 1949. It was deemed unnecessary and cruel. When the heavy horses* are taken to show, often times part of their tail is clipped (just the hair, not the skin and bones). The tail hair is kept longer up on the actual dock, and that is braided or adorned with ribbons.
This picture was sent to me by Lockley Shires in Great Britain. I asked for examples of how they prepare their horses for show. You can see the entire tail is still there for the horse. When this equine retires to pasture, the hair will all grow back and they can use their tail, all of it, the way it was intended. Thank you Lockley Shires!
* heavy horses generally refers to large draught horses like the Clydesdale, Shire and Percheron among others.