Back about 20 years ago, the year I used seven pounds of Goex in the NMA, I practiced fast reloads and adjusted my accoutrements to accommodate it; with a double belt pouch (Mil surplus leather cartridge box) containing wads in one, balls in the other, my flask with measue hanging crossbody and the capper on the flask strap; my load time with powder, wonderwad, ball and cap ran about 90-100 seconds. with just powder, ball and caps it was a little under a minute each on average for three cylinders.
I don't know who made the inline capper but it works with the Pietta .44 like it was made special for it. I did not load one chamber at a time but spun through six of powder, then six of wads or balls, then six of caps. This actually went faster for me away from any table, because there is no tendency to lay something down when standing at the firing spot.
The cylinder change in the Remington should take less than ten seconds and probably nearer to five seconds with daily use.
At that time I could still ride and I'm certain that a cylinder swap on horse back would be easier with that revolver than trying to reload it and also easier than trying to shoot a carbine from a moving horse. (Well, I never had a real carbine but I carried a lever action Marlin on my horse many times, key word being carried, as a kid I had learned that accurately shooting a bow from a horse was much easier than hitting anything with a rifle)
I'm not sure that paper cartridges would be much faster to load, but they would have the supply advantage of always using the minimum charge which could save a lot of powder for an army, and would require less thought on the soldiers part. All those wooden boxes though!
Now with that in mind, I doubt that shooting either revolver or carbine from horse back happened other than in military drill or during a cavalry action. A lone civilian or scout would be hiding or running, gunfights were most often ambushes. The little I know about cavalry tactics from what I've read makes believe that carbines were shot while dismounted and that revolvers were shot during a charge and that sabers were the main cavalry weapon.
Think about how long a charge lasts, say 200 yards run in at about 9-10 yards per second, somewhere between 20 and 30 seconds in which to empty the revolver, reholster the revolver and draw the saber; well actually if you don't shoot until 75 yards only 6-8 seconds.
Once in the melee the revolver would as dangerous to your own troops as to the others as the horses rear and plunge.
Not much spare time to juggle another revolver or to reload, but I imagine, and that's all it is- I wasn't there, that after a very few minutes of hacking and bashing with the sabers that the horse soldiers would break off and put some distance between them and the enemy. Regroup, reload, repeat. Horses are not designed for stand still and fight tactics, they are designed to move quickly. Hit and run.
Why two revolvers? Of course men have two hands and given that all the shooters are moving and all the targets are moving, even unaimed or poorly aimed fire will cause some causalities during that minute or less that closes to saber fighting distance, and of course war horse trampling distance too.