Answer:
Yes, large animals such as horses, cattle and llamas can have convulsions, where they are not in control of their muscle contractions and can strike out powerfully and unexpectedly in any direction. It is a scary thing to see and very dangerous to be around because the animal can hurt or kill you very quickly without ever giving any kind of warning that it is about to kick/lunge/flail in that direction.
Convulsions are a sign of severe central nervous system disease. In horses, convulsions are associated with infection by West Nile virus, Eastern Equine Encephalitis virus, West Equine Encephalitis virus and St. Louis Equine Encephalitis virus. Cattle are more likely to have a toxic poisioning or rabies. Llamas may have rabies, listeriosis, or meningeal worms.