Bear in mind that Terry's Texas Rangers was an unusual command and the skirmish mentioned took place early in the war. Lack of proper armament may explain why so few Confederate cavalry commands were available in 1861 and well into 1862. Lack of effective reconnaissance severely handicapped General Johnston while his army camped about Bowling Green.
If the typical Confederate trooper had possessed even one good quality five or six-shot revolver rather than a single-shot infantry arm, he wouldn't have been at such a disadvantage when fighting on horseback against a Federal horseman armed with a saber or a revolver or a breech-loading carbine.
If this is primarily a discussion of Confederate cavalry arms, there's probably a useful thread exploring this topic on the arms and equipment message board. I have a recent post there concerning Kerr, Adams and Tranter revolvers in Confederate service.