Well, to be technical, wheellocks. 
Niftier than flintlocks! But more expensive and complicated - eventually died out in favor of the cheaper flintlock.
I stand corrected. I agree completely that wheellocks are niftier than flintlocks. Today’s improved metallurgy and better-than-pyrite sparking compounds fairly demand that we revisit the concept.
They will look something like this:
Only, firing bullets. :DThe terms changed over time- the original dragoons were mounted infantry along the lines of the WWI era Australian Light Horse or US Civil War cavalry, but over time, the role and tactics changed.
That’s why I separated the two types into “classic” and mounted infantry, listing the typical sorts afterward).
Little Joe reloaded at least once by switching cylinders in a Bonanza episode. 
Infantry marches to battle and fights on foot.
Dragoons ride to battle and fight on foot.
Cavalry ride to battle and fight mounted.
Hell, I guess they weren’t Airmobile Cav, they were Airmobile Dragoon.
That was a British government scam. Most cavalry during the Napoleonic Wars era were defined as dragoons - regardless of their actual role in combat - because dragoons were considered infantry, and by law infantry were paid much less than cavalry.
There were muskets designed for reloading on horseback - known as Dragoon rifles; and also Carbines.
Some of the designs had captive ramrod designs so the ramrod didn’t get dropped or anything while the user was reloading.
As has been noted though, tactics were very different in those days - while muskets could be (and were) employed on horseback, there weren’t generally people riding about, firing a gun, then spending the next 45+ seconds frantically riding around trying not to get shot while they reloaded to fire again.
Basically you fired your musket, then got in close to mess up your enemy’s day with a taste of cold steel (ie, a sabre). The idea of riding around firing guns from horseback as a standard thing really dates from the mid-late 19th Century when repeating cartridge arms became available - there were carbine versions of several single-shot arms available (The Martini-Henry and Trapdoor Springfield had cavalry carbine models) but tactics of the era generally involved getting off the horse to fire the gun - the shorter length and lighter weight was to make it easier to carry said gun around, not make it easier to act like part of Buffalo Bill’s Travelling Wild West Extravaganza but on the African Veldt or wherever.
Obviously soldiers could and did fire these single-shot guns from horseback and reload them on horseback, but that was really for emergency situations rather than as standard doctrine.
I would note, as pointed out upthread, that the tactic of using guns (Wheelock pistols rather than carbines) from horseback had a much earlier antecedent than the 19th century - the “Caracole” - that dates from the early 16th century.
The idea of the caracole was to combine the mobility of horsemen with firepower to decimate more stationary pike formations. You rode up in a dense column, fired your pistols (one side then the other), wheeled about, and trotted to the rear - to reload (I assume on horseback) and do it all again.
Meanwhile, your poor enemy pikemen stood gripping their pikes waiting for a charge that wasn’t coming, while being riddled with pistol-shot. Eventually they break under this punishment and run - that’s when your cavalry charges (at their fleeing backs) with cold steel! Then the massacre begins.
That was the theory anyway. It relied on exploiting a weakness in early modern infantry deployment: that big blocks of pikemen often had arquebusers only on the wings, not interspersed; so horsemen could ride right up to the center of pike formations and fire their pistols more or less safely.
The caracole ceased being useful when European armies mixed longer-range musketeers in with their pikemen … much easier to shoot a pistol-wielding rider off his horse (or to shoot the horse) while standing on terra firma with a longarm, than for a horseman to hit anything with a pistol.
The caracole fell out of favour and was replaced with the tactics you describe - fire once and charge home (if the enemy was shaken).
Here is a lengthy piece discussing the rise and fall of the caracole:
http://www.investigationsofadog.co.uk/2012/08/21/cavalry-tactics-the-caracole/
The Caracole seems like a firearm-era version of the ancient Cantabrian circle to me…
Dragons fly into battle and don’t need guns because they breathe fire.
Yes, exactly. 
I don’t recall saying the use of firearms from horseback only dated from the 19th century? That’s clearly not correct.
The 19th century was when the use of guns from horseback really developed as a military application, though - you had repeating and easily reloadable rifles, as well as large-calibre revolvers which could potentially take a horse out from underneath another rider if needed.
My point is that it had two ‘peaks’, two periods in which firing guns from horseback was a really useful offensive military tactic - an early and a late.
In both cases, the peak was relatively brief. The caracole died out when changes in the standard European infantry formations rendered it obsolete; rapid-reloading-gunfire-using cavalry died out when cavalry ceased to be used by major powers as an offensive arm altogether, due to the excessive vulnerability of cavalry to rapidly reloaded weapons themselves. Though in both cases, military conservatism kept the tactic going for long after it was objectively obsolete.
What he said, with knobs on it.
Interesting, but… were the cavalry financially responsible for their own horses? Or was that only the officers?
Cavalry got to wear cooler uniforms.
Plumes and tight pink pants.
One wonders about those guys. :dubious:
I have read accounts of Simon Kenton where he could reload his Flintlock while running, the account said that his rifle never ran dry!
Now a flintlock would be the fastest muzzle loader to reload because it will self prime, that is as long as one remembered to close the pan cover (frizzen).
I have one that has a large touch hole and it will reliably self prime.
the powder would be in a paper cartridge or just a palm measurement would be good enough. The spit patch would also be of great importance as it would swab the bore upon loading. I can shoot all day using a spit patch and on the flip side only get 3-4 loadings before a cleaning using a lubed patch.
I use a lubed patch for hunting as a spit patch will be a poor choice to leave in place for an extended period or can freeze also.
So running or riding it can be done and always remember,
“A story is akin to a bottle of wine, the both get better with age”!