What do the horse's messages mean?

As far as I know, the Horse's only purpose is to hint at the "Secret Horse Level", much how Diablo had a cow that could be clicked (though the Secret Cow Level only existed in the sequel).

To clarify, the cows in Diablo also responded when clicked on:

  • "Yup, that's a cow all right!"
  • "I am not thirsty"
  • "Hey! I am no milkmaid!"