This was a question that was ask of me by a Legion member that attended the Cpl. John C.Bishop funeral. I had to confess to him, I did not know. I told him I would try to find out. I started looking with the Google search engine. There I found many answers, Some thoughts dating back as far as 1622, but the one I think makes the most sense is listed below. Within my search I learned a new word, "Caparisoned Horse".
The boots facing backwards in the stirrups was first used in Abraham Lincoln’s funeral. It is said that the backward boots symbolize the fallen soldier looking back over his troops, and that he will never ride again.