This question comes up periodically on a variety of historical forums. Carrying a loaded, capped Remington or Colts revolver cylinder separate from the frame is so egregiously stupid that you don't even want to think about it, no matter what a movie script writer may have had a actor do. It is effectivly a hand grenade, People at the time didn't carry spare cylinders, they carried spare revolvers. There are good historical accounts of Confederate irregulars -- Mosby's people, for example -- carrying four or five; two in holster belts and two in saddle holsters were comon. If carrying a spare cylinder for reloads was safe, the contemporary manufacturers would have sold them with their guns. They didn't. The "bible" for Civil War arms purchases is Executive Document 99, 2nd Session, 40th Congress (14 January 1868). In Ex Doc 99, the President transmitted a War Department report to Congress on the War Department's purchases of arms during the Civil War. There is nothing in the report to indicate the the Federal Army purchased Colts or Remington revolvers with spare cylinders. One can't say that a few individuals didn't have spare cylinders fitted and carry them on their own (getting back to my egregiously stupid comment), but it wasn't institutionalized. For a reenactor to do so is clearly farb; stupidly so
As for issue weapons, one revolver was the norm later in the war. Early in the war, many cavalry companies were armed exclusively with sabers.
Regards,
Don Dixon