https://civilwartalk.com/threads/a-question-on-cavalry-firing-carbines-from-horseback.177517/
From "Lampass Bill":
Cavalry skirmishers often fired their carbines from horseback, usually when at the halt. During Price's Raid in 1864, most of his men were armed with infantry rifles. They generally fought dismounted, but not always; at Mine Creek, Kansas, Marmaduke's Division, being pursued by Federal cavalry, formed a mounted battle line while halted. This give them a chance to reload from the saddle, and they temporarily halted a Federal charge, but the Yankees rallied and charged home with sabers and routed Marmaduke's men.
Here's an example of a fight with firearms near Doniphan, Missouri, during Price's Raid, as recalled by Sergt. J. C. Steakley, 3rd Missouri State Militia Cavalry:
The enemy made their attack from the north, where they were formed in a terrible thicket of timber, large and small, interlaced with underbrush. They were about one hundred and fifty yards from us. We charged at once and they counter charged. We were fighting up on an ordinary 'point' ridge, high in the center, and by the time our third charge had been made our command had become divided. . . . We seventeen men on the east side [of the ridge]
had enough to employ us, for we were only about thirty yards from the Confederates and plenty of them in front of us too. I glanced around and saw that I was the only officer of any rank there. "Let's charge them once again!" I shouted. "Come on, boys, let's give 'em hell!"
Oh how badly we needed our sabers and how we wanted them! The seventeen of us dashed right into their midst. But we were not fighting 'paper collars' or 'greenies'; we were fighting Joe Shelby's veterans, who knew nothing but fight. I emptied a double-barrelled shot-gun and two eight-inch revolvers at them and then called to the men to stop and form and load up, as I knew that their weapons were about all as empty as my own.
We formed up and began to load up, when it seemed as if providentially, I dropped the pistol caps which belonged with a bunch of cartridges. I slid from my saddle and while stooping to pick them up, happened to glance beneath the underbrush. . . . What did I see but one hundred or more of the enemy advancing upon us in line of battle. It was evidently another command which had come up the river, heard the firing, found our camp, and pursued us up the ridge on our rear. I picked up that bunch of pistol caps, sprang into my saddle and shouted: "Boys, this won't do. Look yonder. Let's get out of here!"
Our guns were empty. I directed one of my company buglers to run out eastward about one mile and stop, so that we might load, none of us having even two chambers of a pistol loaded. I learned subsequently that the bugler and a private who went with him never stopped till they reached Poplar Bluff, fifteen miles or more away. . . . .
If we had had our sabers we would have been able in the dense underbrush to slaughter them in the confusion; for they were mounted, their lines were in no sort of order and their long guns were empty. However the fourteen men with me said they would follow me where ever I went. I assured them that if they did, I would take them out safely or die in the attempt.