I grew up spending every minute I had working with any horse I could get near and watching anyone that had well trained horses. This was in the late 1950s. I watched a dressage and jumping trainer from Germany (came over after 1936 Olympics) that was very harsh. I watched, and years later worked little with, a Polish dressage trainer that also fled Hitler. He was much kinder and got a lot more done in my opinion and he had a LOT happier horses. I watched cowboys that 'broke' horses like it was all a big rodeo. Definitely not what I wanted nor did I ever find it necessary or advantageous.
I was convinced that you could 'teach' a horse to do anything he was capable of doing. So I watched and worked and handled and rode any horse that anyone would let me handle or ride. I soon found out I had a 'knack' to get more done than all of the professionals around where I lived. By 13, people were paying me to ride their horses.
I watched herd behavior and saw how horses responded to each other. They validated everything I had figured out.
When clinicians started doing the kinds of things I had done for a long time, I thought - "Gee. Why do they think they invented this. This is how horses have always learned if someone just tried to teach them."
I also figured out that I needed to train two totally different ways. One way for horses that were not spoiled and a completely different way to stop bad behavior and 'retrain' spoiled horses. I found out that you needed to not only 'interrupt' what you did not want but you had to find a more definitive and effective punishment for behaviors that a horse did not want to give up.
I figured out that a horse craves constant and predictable responses. A horse likes 'sameness'. When I read that a horse is bored, I know that either the rider is bored or is irritating the horse. This is also why a spoiled horse will often times fight tooth and nail to continue the same wrong behavior.
I also figured out that horses really do not naturally like 'contact' -- even with other horses unless they are mutually grooming each other. They can be taught to accept and eventually like people contact, but when they have not been handled a lot, the thing they like best is to not touch them.
I am convinced that many species are smarter. I have trained cows (some to ride) and I think they are smarter. I have raised bison (have 2 now) and they are a lot smarter. Pigs are the smartest of any animal I have been around (also proven by scientific testing).
I think horses are the most useful and 'trainable' of all these animals because they are easily intimidated and naturally do not like to be touched. I think that is why a touch or 'pressure' can easily cause an action or movement and the withdrawing of the pressure or touch 'release' or 'relief' is the only reward a horse needs.
As a prey animal, pressure is always a threat and the withdrawing or release of that pressure is the relief. Food is never a reward. Yes, it can be conditioned into any animal including a prey animal like a horse, but it is not 'natural'. It is a taught response. So, to me, it is not nearly as natural and not nearly as effective as the release of pressure.
I have also found out that when you replace the pressure with a 'non-pressure' stimulus like a smooch or body language (like horses do to each other) instead of a touch (kick, whip, spur or???) you have a happier horse. Horses to not start wringing their tails from a smooch or from using body language like they do from too much contact with whip, heel or spur.
I think most people 'over-think' training and over-think a horses reasoning ability. Horses respond in a very basic and rudimentary way when you understand how they teach each other how to be an accepted herd member. Their thinking, to me, if very simple and basic and VERY predictable.
If we stay light with our stimulus, a light touch of only an ounce or two is all it takes to teach a horse to move away from that pressure. We are dealing with a very thin skinned animal with so many nerve endings in their skin and the ability to move and flinch their skin, that a fly elicits a response from most horses. Why would a person have to use more pressure than that? I think horses are many times more sensitive to pressure than any other animal I have worked with and much more sensitive than people. They just naturally do not like touch. I am convinced they have to be taught to tolerate it. I am convinced that all of the petting and feeding treats and praise are less effective than releasing pressure. I am convinced that all of this is for people and not a benefit for horses although they can be conditioned to it.
So, Now, all of the people who are convinced otherwise can respond.