I don't know if you have ever heard the story of the crafty fox and the flock of ducks. The ducks were in the river and they were alert. The fox sent a little twig down the river in the midst of them. They were alarmed by the first twig. But as the fox continued to send twigs down the river, the ducks grew accustomed to them. The fox gradually sent bigger and bigger sticks down the river until he was able to ride down on a log into the midst of the now-relaxed ducks. One poor duck paid for their inattentiveness with her life.
Maybe you haven't heard the story of the fox and the ducks, but I am pretty sure every horse has been told this story. Every waving branch and rustling grass and certainly every plastic bag (oh, no! The terrible horse-eating plastic bags!!!) is potentially a sign of a predator. Any thing that traps them or interferes with their ability for flight can be an uneasy place to be (like horse trailers, bridles, etc.). And every human, with eyes set in the front of his head like other predators, has all the markers of a predator.
A horse, because they are a prey animal, is born with suspicion toward the unknown and toward predators. It is in their blood. Then, depending on their life experience, they either learn to identify things/people as friends and protectors or as life-threatening enemies.
The second thing about how horses think involves what the horse wants. Horses, like humans, have certain things that they want and they will move to the easiest way to get what they want. They also have certain things that they don't like and they will avoid those things.
Horses like to feel safe. They look for the safest place to be. This makes sense when you think about the fact that they are prey animals. Safety is a big concern.
Sometimes safety is found in the company of a human. We are the top of the food chain around here, and, if they horse trusts our leadership, then the safest place to be is with us. If you can imagine going somewhere with the biggest, toughest guy in the world (knowing that he will look out for you), you can imagine how safe a horse feels with a person whose leadership they trust.
Sometimes safety is found in the herd. There is safety in numbers, in extra sets of eyes. A horse who feels safest with his herd, will do his best to get away from his rider and rejoin the other horses.
Sometimes a horse feels that his best bet is in himself. There is no herd to save him. That horse will do his own thinking (or his own panicking) independently of the human trying to direct him.
So horses like safety. They also like things that make them feel good. For example, they like to eat. Some horses like to move as little as possible (like WhiteStar -- her idea of a good day involves standing in one place and over-eating). There are just certain things that feel good to a horse.
Horses also like playful interaction. They like to do things together -- fun things. A horse, even a horse like WhiteStar, would not be perfectly happy by themselves in a field with nothing to do but stand there and eat. They like to have some good interaction with somebody else.
The third thing that my instructor taught me is that horses have their own way of communicating. It's a slightly different language than the one that humans typically use. If you ever sit and watch horses in a field, you will see some of the things that they say to each other.
You will see two horses standing by each other, flicking their tails across each other to swish away flies. This is two horse being friendly. They are both helping each other out and the two of them are more comfortable together than they could be alone.
Sometimes horses are just standing together. They are all relaxed, just contented to enjoy each other's company -- like friends who are such good friends that they don't even have to talk.
You will see horses moving each other. They use pressure and rhythm to tell each other where to go. They will glare or pin their ears or stamp a foot or nod a head. They will push. Sometimes they nip or kick. These are ways that horses communicate in a field.
The fourth thing is that horses are individuals, just as people are. Above and beyond the basics, each horse has his own worldview based on his personality and experience. As you work with a horse, you get to know that horse and you can meet the horse on his own level.