I have two original Remington New Army revolvers. One made in 1863 has been with me for about 20 years. The other made in 1864 came to me recently. Both are entirely functional, a testament to the designer (Beal) and manufacturer (Remington).
The cylinders of my two revolvers are indeed interchangable, as are the base pins (which retain the cylinders and on which the cylinders turn), indicating a high degree of maintaining manufacturing tolerances 150 years ago.
The process of actually changing out cylinders requires several steps:
1. hammer to half-cock
2. unlatch loading lever, but the ball ram cannot be permitted to pass through the frame into a chamber
3. remove T-shaped base pin
4. remove cylinder
5. insert cylinder
6. replace T-shaped base pin (making sure it is correctly oriented; if inserted upside down it will not be possible to seat it and removal to correct can be difficult)
7. return loading lever to latched position
Assuming the replacement cylinder has been loaded and capped the revolver is then ready to cock and fire. As Magneto pointed out, carrying a loaded and capped cylinder could be rather dangerous; dropping it could result in one or more rounds firing, as could a moderate impact on the percussion caps, and no possible control over where the bullet(s) might go.
Using a cylinder with powder charges and balls, but uncapped, would require placing percussion caps on the 6 nipples after making the change. With a capper device this would add perhaps another 30 seconds or so to the reloading cycle.
I think it would take me at least 2 or 3 minutes to perform such a cylinder exchange. That time might be improved with regular practice, which would also have to include training myself to correctly orient the base pin during reinsertion. But I doubt if it could be done in less than a minute or so anyway, and doing this during an actual gun fight would be very difficult.
Personally I would much prefer to simply have another revolver, or even two or three more, just like many of the old timers did back in the day.
Worked with a cop years ago who had spent several years on the NYPD in the 1960's. He refered to this as the "New York reload", simply drawing your other gun.