Cosmoline is right
Although western movies show every cowboy sporting one or two Colt Single Action Army revolver, the actual historical evidence overwhelmingly shows that they were quite rare on the frontier in the time period we now know as the "old west."
Consider that the modern revolver didn't really appear l until the 1850s. Colt's "Paterson" of 1836 was a commercial failure. The famous "Walker Colt" horse pistol of 1847 was great marketing, but very few were actually made, and they were "horse pistols" -- so big and heavy they could only be carried in pommel holsters on a horse. The first commercially successful revolver was the Colt model of 1851. It was followed by rapid development from both Colt and Remington of various models, culminating in the Colt 1860 Army and the Remington "New Model Army" that appeared in 1863 (and is erroneously referred to as the "58 Remington" because of the 1858 patent date on it). It wasn't until after the civil war that these revolvers began to show up in civilian hands, and then only because of surplus from the war, and surplus manufacturing capacity left over from the war years.
The winning of the west took place following the civil war in the "Indian wars" era that lasted roughly from 1865 to 1890 (and Wounded Knee, the last major battle of the Indian Wars). In the early part of that time, the dominant guns on the frontier were muzzle-loading shotguns and rifles. Rich men may have had a metallic cartridge long guns like Sharps or Remington rolling blocks. A few lucky souls might have had repeating rifles like the Henry, or the Winchester 1866 (Yellowboy) or 1873. Those who had revolvers generally had cap-and-ball sixguns like the Colt 1851 or 1860 or the Remington.
The first successful metallic-cartridge firing revolvers appeared in the early 1870s. Medievalmax is mistaken when he says:
medievalmax said:
Compared to the more recent models where you had the option of breaking the gun open, exposing the entire cylinder,
Actually, the very first commercially successful metallic cartridge firing sixguns were break-open designs. Smith & Wesson made them, and had the market to themselves until the Rollin White patent (on bored-through cylinders), that S&W controlled, expired around 1871. At that point, Colt and Remington could finally get into the game. Smith & Wesson had already been producing top-break revolvers for years by the time Colt introduced the SAA in 1873 and Remington its competing revolver in 1875. And in fact, the Colt wasn't available to the civilian market for several years later as Colt was selling its entire production at least through 1875 to the U.S. Army.
The U.S. Army did consider the S&W top break to be an advantage, at least for the cavalry. Major Schofield actually tested the S&W Model 3 and made several recommendations for changes that would make it better suited for use by cavalry, resulting in the "Schofield" model of 1873.
In practice, you can certainly reload a top-break revolver quicker than a soli frame design like the Colt or Remington, but only because you can eject the empties so much quicker from the top-break.
Double action revolvers weren't far behind, actually. Colt's first successful double action was released in 1877. There were double action cap-and-ball revolvers before then. I don't know when the first solid frame swing-out cylinder design came along, but I don't believe it would have represented a significant advantage over the S&W top break models that had been around since 1870 or so.
As for what the "cowboys" carried, the average cowboy (or vaquero, if you prefer) would have had a carbine, if he was armed at all. A repeating rifle like a Henry or Winchester (or later, a Marlin) was much more useful on the range than a revolver. Those that carried revolvers generally carried cap-and-ball revolvers or homemade cartridge conversions of them, because they were so much cheaper and easier to get than new Colts or Smith & Wessons.