My understanding is that military procedure in the mid 1800's called for shooting the revolver in you left hand. I think it was Civil War Times that did an article on this in the late 70's or early 80's. I probably still have that article somewhere but doubt if I can find it.

Their reasoning was along these lines.

First, look at holster design. Holsters were designed for left hand cross draw. Had to be because the saber was on hung for a right hand cross draw. A butt forward holster is easier to draw with either hand. The holsters rode high on the belt. A cross draw holster is much easier to draw from mounted if you holster is high on the belt.

Numerous after action battle reports from the official records were quoted and cited that mentioned an individual "Taking his revolver in his right hand". There would be no reason to specifically mention this if right handed shooting was the norm. The implication was that the shooter chose to fire right handed, because in that case accuracy was more essential that Army regulations.

Interestingly over half of the references to revolvers being used in combat were by artillery troops. Revolvers were used for counter cavalry defense, much the way we used M2 Brownings for ADA when I was in FA.