Horses can’t vomit, they have a part in their stomach that prevents them from vomiting it's called the cardia. In case of too generous a diet or in this case of absorption of toxic foods, the cardia and the esophagus will prevent the evacuation of food. If the horse tries to vomit, it’s likely to be asphyxiated.
After what the horse has swallowed, one should consider either a treatment to avoid any gastric problems (colic, twisting intestines) or in the worst case an operation.
Good question, bye