I know several ways to ' teach ' a horse to lay down
One way is time consuming and you must have your horses cooperation.
All you need is a headcoller/halter and a 2-3 meter rope, it is also made easier if you work in a sand school.
With your horse wearing the halter with rope attached, stand on the near ( veterinary left ) side , have the rope passing over the horses back/withers and attach to the offside ( vet right ) .
If you pull the rope this should bend the head away from you - this will mean that when the horse lays down its legs will be pointing away from you - very important as you don't want to get kicked by accident -
Stand at your horses nearside shoulder facing forward - ask for the nearside foreleg - hold the nearside foreleg in your right hand and the rope in your left.
Start by leaning backwards, pulling on both rope and leg - when your horse ' leans back ' release and reward ( so you are rewarding your horse for doing what you want ) , repeat this process moving further backwards each time - putting more backwards pressure on the rope and leg, rewarding each time your horse leans further back. If your horse co-operates then eventually it will kneel down , then lay down fully.
Basically all you are doing is unbalancing your horse and rewarding it when it moves in the direction you want - so your horse will learn what you want. Don't try to do it all in one day - it normally takes a week or three depending on your horse.
You don't need to tie your horses legs up , and as your horse makes the choice to lay down it is not what I would call harsh in any way, it is a harder process from a human perspective and takes longer, but it is kinder to the horse.
Any idiot can force a horse onto the floor - this is not training a horse to lay down , just forcing one to lay down.
With training you should be able to ask you horse to lay down by ' tickling ' its ' arm pit ' . This can be done either on the ground or mounted.
Stand at the shoulder Aladar 006.jpg
Ask for the leg and lean back Aladar 007.jpg
Horse on the floor Aladar 008.jpg
Same horse but with me niggling his leg pit with my foot Aladar 031.jpg
At no time did this horse have its legs tied up - and as you can see no force is needed.
By the way this horse was taught with the head pulled towards us , not with the rope over the back which is safer