They may be so weak they cannot stand up. They can't eat and they drool because they can't swallow. Their tail may lose it's tone. They may walk stiffly with a short stride or they may be weak and stumbling. Eventually they die because their respiratory muscles become paralysed or because they get other health problems from being down.
Horses can get botulism in any of three ways.
In foals, botulism can occur if the bacterium grows in the foal's intestines. Foals that are growing well and are being fed grain are most likely to get into trouble. Occasionally a wound can become infected with the bacterium and cause botulism in adults. Fortunately, this is rare. Far more commonly, botulism occurs when horses eat contaminated feed or water.