As I understand it horses would in general be employed with the artillery as they would be more inclined to accept the carnage of an engagement. But mules,perhaps because of their superior intelligence would absolutely go ballistic and often become near thoroughly unmanageable when subjected to an engagement.

It is an interesting subject. Both horses and mules would have to be trained for whatever their job may have been. Just like the new cavalrymen there would have been a period of adjustment for both. And that heard mentality of the animals would most likely have remained throughout the war. If one runs the remainder would all be inclined to follow. Perhaps this would explain some cavalry routs.