Horses cannot throw up, except in extremely rare occasions.
Technically, horses can vomit, but it is very uncommon and unlikely to happen, due to the horse’s anatomy.
A 2001 USA Today article summarized it this way:
“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.”
Source
Why horses can’t throw up (April Holladay/Wonderquest, USA Today: May 3, 2001)