With rifles, IIRC one commonly dismounted to aim, a tactic much disparaged in popular history but which indisputably worked, or did for the Eastern tribes out on the Plains. The time required for that process being much overestimated. There are numerous accounts of mounted Plains Indians either hovering outside of rifle range in a sort of standoff, or of attempting to empty the rifles of the opposition by riding across their front.
One of my favorite retellings of an incident like that was told by Teddy Roosevelt while he was in the Dakotas. Obviously, by the time he was there, most of the Indians were "pacified" but there was still plenty of danger to loan travelers if they happened to run into a young Indian buck or two who were out on a lark.
Roosevelt was out looking for some of his cattle when he saw four mounted indians at a distance. They saw him and charged at him with apparent bad intent. Roosevelt dismounted and drew down on them with his big Winchester causing them to draw up instantly.
His quote was something like, "It takes an inordinately brave man to charge another drawing a bead on him with a rifle."
