What is a common allergy for horses?

It all depends on the horse. Some are allergic to dust, some even to hay. There are, however, plants that are toxic to them. One major one is Black Walnut. Even the shavings (if they are just stood on) can kill a horse. I sugest doing to reseach on this, as there are a lot of poisonous plants. Most horses won't eat them unless they are really hungry or young.