This is a combo reason:
"al" = "a + el", so this is "El caballo ve a el gato" (although in Spanish, you must contract to "al").
There is something called "the personal 'a'". Basically, you add an "a" when the verb applies to a person (or a pet). In this case, the horse is seeing the cat (who is personified), so you say "El caballo ve a el gato" (which actually must be "El caballo ve al gato").