The fact that the horses got stuck in the mud actually only served to prolong each wave's exposure to arrowfire, causing routes before they could reach the english line. Was it something like 15 charges made over the course of the whole day? Imagine that... "But it's MUDDY, Sir!"
I saw a computer simulation of the battle with regards to the mud and they showed the horses falling into each other like dominos, because there was so many, and leaving the knights incredibly exposed and stuck. *shrug*