No, positive reinforcement does not work on every animal. It works on dogs, people, and other predator animals because they are naturally praise oriented, they want to work in a group or pack and do good. Horses, and many other prey animals, are physically not this way. They want COMFORT first. Example: How do you ask your horse to go? You squeeze/tap his sides. It doesn't matter if you say 'good boy' or not after he walks on--the only reason he moved was because you released the leg pressure, not because you praised the horse.
It is a nice idea to think that every animal works with positive reinforcement, but it just is not so. And it's not what I think; it's how most prey animals are hardwired. You say your horse is a good example--can you ride your horse without a bit, bridle, saddle--absolutely nothing, no ropes? And direct him only with voice, or maybe a simple touch? I'm not trying to sound mean but I doubt you can; to work through SOLE positive reinforcement would mean you cannot ride a horse with a bit; that works by negative reinforcement. So does a halter, spurs, leg pressure, ect. The horse gives, the pressure goes away. That is negative reinforcement training. And it works well for a reason; horses do not want praise or petting, they want comfort. Which is to be left alone (ie, why the majority of horses would rather say in a pasture then be bothered with people!). There is nothing wrong with this kind of training, it's just that people sometimes think it's wrong because people think horses are like them; people think horses want, crave, and need praise, because people do not like doing jobs without praise (words, touch, money). Simple fact of the matter is, horses are not people. Horses are not predators. There is nothing wrong with the way they are being trained, and you don't have to beat your horse with anything to get it to do things. If you go through the steps logically, your horse will rarely fight because you taught him well.