When you naturally think of the horses in the military you would think of the Cavalry and Artillery Horses. I once read that in a single four gun Artillery battery, they had a compliment of 120 men and 175 horses, that were necessary to not only pull the guns themselves, but also the extra Caissons ammunition Limbers, Battery wagons and ammunition wagons.
But the majority of the horses were used to move the supplies. While you would not think that these animals would not be subjected to the dangers of the Battlefield, but their work was no less hazardous. There are many accounts of these animals simply dieing in their harnesses because of exhaustion from what they were put to while on those marches.
One account that I have heard of was of the Cavalry remount post in Washington DC which at one time had 50,000 horses at that depot. This is not an extraordinary figure when you consider that every Union Cavalry regiment usually maintained 3 horse for every man in order to keep the regiment functional because of the losses that they would suffer.
The Old jokes was that a horse will do their duty every 45 minutes and that is the reason that Washington DC is called the "Crapital", because of all the Horse that were in the city during the war. But the 45 minutes to do their duty is true. Which gives another aspect to the poor guy who had to clear the barns.
This also leads us to another understanding that during the later years of the war and after, in the south, there were no horses to be found to farm the land.