Interesting question. Prepare for a hoard of angry formers accusing you of what is apparently the worst possible sin: anthropomorphizing.
For some reason, people can get really defensive when we try to prescribe animals emotions. I don't see why, personally. Aren't people and animals more similar than we are different?
For example: If I were a horse and I saw a disappointed and depressed human, maybe I wouldn't get it. Horse me would sense something is wrong, but the human may express disappointment in a different way then I, as a horse, do. Just because disappointment -- or any emotion really -- is expressed in an alien way doesn't mean it isn't there. Or that it isn't indeed disappointment.
Most humans are disconnected from herd instinct and body language. After all, we have verbal language. Verbal language is amazing and communicates very effectively. Because of verbal language's effectiveness, body language has become a "dead language" among people to an extent. Maybe this has disconnected us from the emotions of non-verbal animals?
Anyway... I believe horses do feel emotions. Horse emotions and in horsey ways, however. Horses can feel anger, frustration, and rage. I once tied a horse who knew how to break ropes and runaway because he didn't like to stand still. He radiated
frustration. He pulled back, lightly, several times. He tested the waters. Suddenly, he snapped. He bucked, he bit the rope, he kicked the tree he was tied around. After that didn't work, he went through a phase that struck me as similar to human disappointment. Like a petty child sitting in a corner.
Some people are naturally "horse people" and understand horses very well. I theorize that some horses are naturally "people horses" and understand people very well and people understand them. I have a mare who has an honest competitive
spirit. Competitiveness is such a human trait, but my mare seems to have something like it. She knows (because I tell her, via body language I suppose) if we win or lose. When she realizes we are losing, she kicks it up to another level. She finds her second wind of speed and power. Once she's back on top, she quiets down and seems to radiate a sort of horse happiness. Maybe even horse self-satisfaction.
If this sounds crazy, think about how some people are a bit "horse like" themselves. Some people are extremely empathic, read body language very well, and are so in tune with others that it's almost like they're mind readers. I myself have a couple "horse traits" -- maybe a part of an ancient herd instinct before language was refined? One of my friend's brothers was hurt in a football accident Friday night. I didn't know this, but I felt very "stirred up" for some reason and worried. I texted me friend, and she told me she was in the hospital with her brother. Weird, huh? My friend's emotions being transferred to me didn't require language at all.
In summary... Yes, I believe horses experience emotion. And I also believe that people can take part in a horse's emotional experience sometimes. Since horses "speak" with emotion, maybe we can speak horse and horses can speak human.