Just thinking about the numbers of horses used is staggering. Even if we go with the battery having only 2/3 of their TO&E of horses, that's 80 per battery. And how many batteries were in the combined US and CS Armies at any given time? And then you add in cavalry mounts, horses for commanders and staff officers, runners, quartermasters, ordinance, engineers, ambulances, replacements waiting to be allocated, and it's pretty easy to go cross-eyed at the idea of counting them all. Granted a lot of the mounts for pulling wagons would have been mules, but even if they are taken out of the equation, it would still be an almost unfathomable number of horses used.
And then they need to be continually bought so the military can replace them, so they are being bred somewhere.