If you are a well brought up person, and someone does something nice for you, you say thank you!
In dressage training, the thank you is in the release of pressure, which is why it is SOOO IMPORTANT that after ever aid, you have a release, it tells the horse that when he responds the pressure comes away. If that doesn’t happen, and happen in the instant that your horse yields, you are not training, you are merely punishing, and confusing your horse, and he will not yield next time, because why should he?
Horses pick up on more than we realise, and sometimes it is also important after a good ride, to say thank you to your horse.
For me, it can be performing a solo performance of the “dirty dancing theme song”, but for others it can be simply just taking a minute and showing your horse how grateful you are.
Others might think you are nuts, and good for them, your horse will understand, and appreciate that you know what he is, and what he does for you.
A huge inspiration for me, classical trainer Sylvia Loch, talks a lot about touching the horse, patting the horse after they respond well, and that in the touch the horse connects with the rider, and finds reassurance and encouragement.
Release the pressure, pat your horse, tell him he is important, never forget that like us horses sometimes need to be reminded that they can do it, that they are special, that what seems impossible now, will become easy in time.