Actually, horsemen used pistols from a very early time, whether single persons or units.
The military caracole as it is usually understood today developed in the mid-16th century in an attempt to integrate gunpowder weapons into cavalry tactics. Equipped with one or more wheellock pistols or similar firearms, cavalrymen would advance on their target at less than a gallop in formation as deep as 12 ranks. As each rank came into range, the soldiers would turn their mount slightly to one side, discharge one pistol, then turn slightly to the other side to discharge another pistol at their target. The horsemen then retired to the back of the formation to reload, and then repeat the maneuver. (from Wikipedia)
True, but the article specifically mentioned repeating pistols, that restricts the time frame significantly.