Handguns during the Revolution days were an officer’s arm ..
were a joke, period.
The preferred weapon was the saber, and for very good reasons.
The saber as you mention was more in their hands for fighting, but a pistol from horseback was much easier to use than a rifle. Pistols were what cavalry carried in pommel holsters up until the size could be reduced.
You had pistol in one hand that doubled as a club after firing alongside the saber.