It is a physical impossibility for horses to throw up their food. Their digestive system is designed in a way that makes them unable to vomit, for any reason.
When a horse eats, the opening valve is relaxed and allows the food to enter their stomach. If there is any pressure from the stomach, like gas or a bunch of food, it pushes the valve tightly closed to prevent that food from coming out.
Horses are unable to do this and if they ingest something that causes extreme gas or is poisonous, they cannot expel it by vomiting. The toxin will remain inside their bodies wreaking havoc
You should never, under any circumstances, give your horse something that is meant to make them throw up.
The trick is to be aware of this fact, understand it completely and always be on the lookout for signs of distress. Your horse will let you know when something is wrong but it is up to you to get them veterinary help when they need it.