The Texas Rangers certainly acquired something more powerful through the expedient of writing letters to Samuel Colt!
The Texas Lone Star republic acquired all kinds of early breech loaders like the Jenks and also revolving rifles, shotguns, and Colt Paterson revolvers. Some of the Colt Patersons were apparently used in battle with the Shoshonean-speaking Nermernuh/ Comanche at the Battle of Bandera Pass, where they caused considerable surprise, apparently. The Colt Paterson was flimsy, lightly constructed, and temperamental. There is an anecdote, possibly true?
that during the bloodbath at the Council House fight in 1840 in San Antonio, one of the desperate Comanche chiefs grabbed a Texan's Colt Paterson by the barrel and wrenched off the barrel from the frame, held on as it was by a metal wedge... The Texas Navy used the arm for officers and boarding parties and such, and so when news of acts of piracy, *ahem,* erm, naval battles in the Bay of Campeche between the Texas and Mexican navies reached the East Coast, Sam Colt had engravers develop a roll-engraving of the events on the cylinder of the .36 that ultimately became the 1851 Colt Navy.
In the case of Texas Ranger Walker (no, no!
the original one! ), he advocated for what became the massive .44 Colt Walker, and after product-improvement, the Dragoon series. A Comanche war shield was a couple layers of buffalo hide, often with shrunk rawhide on the front face, backed with prairie grass, and so the Colt Walker basically fired a .44 cal. carbine cartridge. It was the most powerful handgun in the world until some freakish prototypes at the turn of the 20th Century and the development of modern smokeless powder "magnum" calibers in the 1930s. It was subject to hard wear from the powder charge and became prone to catastrophic failure over time... Hence the Dragoon.
Bottom line: I'd agree with
@Story that this was a long-in-the-tooth and greatly surpassed revolver by the time of the Civil War, particularly among people keenly interested in firearms and the latest, most innovative examples of gun technology. I'd expect to see almost no Colt Patersons used in the Civil War...