I don't remember this very well and my copy of Bernal Diaz's memoir is half a continent away, but I think that most of Cortes men were not "cavalry" as such. Some had horses but most were on foot. Also, I seem to remember the Aztecs that attacked them in Tenochtitlan were basically a mob at that point, armed with makeshift weapons. It goes without saying that they had the advantage of knowing their own city better than the enemy, but the general point is that they didn't fear the guns and horses of the Spaniards as much as is commonly believed.