Nozzelnut
For the Model 1873 Single Action revolver, it would have made sense to set the reloading sequence up for the right side. Since a majority of people are right handed, the ability to reload from that side would have been the most logical and efficient means possible, short of a top-break design. Also more natural for a man on horseback (cowboys and cavalry troopers), to accomplish.
An interesting sidenote is that the French Model 1892 Lebel double action revolver, had the cylinder swinging out on the right side of the frame. Supposedly the reasoning behind this design was that the principal weapon of the cavalryman was his saber, not his sidearm.