Those guys weren't as safety conscious as we are today
Remember that Flintlock Muskets were primed from the cartridge, at half cock, and then loaded. If the cock slipped off half cock on a worn lock or something gave out, oh well , say goodbye to some of your fingers or a hand. I get the chills just thinking about having my hand over the muzzle, ramming a cartridge down the pipe on a primed and half cocked musket. Then again I'm not facing a Battalion of Redcoats either.
Carrying a pistol capped on half cock or with the hammer down on a cap was the least of those guys concerns. Also, they didn't load up until combat was expected, even if the day prior or hours prior.......or even when the troop lines were forming up just like Infantryman with rifles or muskets. No one was riding or walking around for extended periods with loaded weapons.
It would have been situationally dependent. If you were in Indian Country and ambushes or bushwacks were possible, you'd have loaded and capped pistols. If you were a Cavalryman in the Mexican War, where it was pretty well known when a Mexican Division was located somewhere, you'd load when battle was joined.
The nipple cover, or cone cap, or whatever it was called that was on a chain hanging off the Enfield rifle also covered the percussion cap, so it was safer to carry with the hammer on a capped nipple. So maybe something like that was sometimes used.