If the numbers in the Wiki page are accurate, Remington made about 200,000 of these revolvers, many y of them with a cartridge conversion. While they might not have been the most common revolver on the frontier, it would seem with numbers like these, they were not uncommon. Every-damned-one of them had an octagon barrel.
Famously, one of the most well-documented Remington revolvers was owned by no less than Buffalo Bill Cody, who gave the revolver to a ranch foreman, with a note "It never failed me."
Bill's revolver is a percussion model, but there is no reason to think that he would have been unfamiliar with cartridge conversions. Buffalo Bill was a forward-thinker in a lot of ways.
We tend to forget that the period from 1850-1900 was a huge time for firearm innovation. We went from cap-and-ball muskets to smokeless powder and reliable repeating firearms. It was a time of great innovation, and manufacturers large and small were making firearms for the market. I suspect that there were also gunsmiths all over the country making conversions from percussion to cartridge revolvers. Many of these firearms may be lost to history, and examples are hard to find, but even Remington and Colt found a market for conversion revolver. It is not unreasonable to speculate that gunsmiths all over the frontier were converting old-fashioned firearms of every type to the new ammunition.
We know for a documented fact that Remington was producing the 1858 as a cartridge revolver as early as 1868, long before Smith and Wesson and Colt This was an iconic firearm, the first of the new evolution, and I suspect that it was not uncommon to see it on the frontier. Even such a luminary as Buffalo Bill carried one.
UPDATE** Thanks to commenter, Nate, it seems that the Buffalo Bill Center for the West has a very nice example of a factory cartridge conversion in their collection.
That is a very nice example of a factory cartridge conversion.