Horses have a band of muscle around the esophagus as it enters the stomach. This band operates in horses much as in humans: as a one-way valve. Food freely passes down the esophagus into the stomach as the valve relaxes but the valve squeezes down the opening and cuts off the passage for food going back up.
Horses, however, differ from us because their valve really works. Humans can vomit. Horses almost physically can't because of the power of the cut-off valve muscle.
Also, the esophagus meets the stomach at an angle which enhances the cut-off function when the horse's stomach is bloated with food or gas. Then the stomach wall pushes against the valve, closing the esophagus even more completely from the stomach. Normally, the mechanics are such that the horse's stomach ruptures before the valve yields.
If the material does pass from the stomach out the esophagus, the horse is dead or nearly so. That's why horses can't vomit. But, sometimes they do. Rarely, to be sure.
Reference Link:
https://prezi.com/_umd75jgjizz/why-cant-horses-vomit/
http://usatoday30.usatoday.com/news/science/wonderquest/2001-05-02-horse-throw-up.htm