It never really occured to me that Civil War cavalry would be issued more than one revolver. I sort of assumed any extras were taken off dead enemies or friends or stolen from captured supplies.
Keep in mind that the famous walker Colt and the Colt dragoons were not intended as "sidearms" in the sebnse of being worn in a holster on the side of the bearer. They were intended as horse pistols, to be carried in a scabbard slung over the mount's withers. My recollection is that the Texas rangers each carried two Walkers, one on each side of the horsie ... but I don't recall where I read that.