Hi!
One of my favorite movies! I suspect he had a Colt 1873 SAA clone made by Uberti. He also used an 1873 Winchester (again, may have been a clone by Uberti), probably in 44-40 (a lovely cartridge to be sure, but definitely underpowered for that part of the county, in my opinion). I always thought this choice of firearms for him was rather unrealistic. After all, the film was set in contemporary times, so a more modern, stronger and more powerful single action pistol, like a Ruger Blackhawk in 44mag or 45colt (able to handle modern high end ammo, unlike the colt/clone) and a lever action rifle like a Marlin 1895 in 45-70 would be both appropriate and make better sense for someone in his line of work given the 'wild life' one might need to contend with in that part of the country.
I realize the film makers were trying to make the character look more like an throw back old time cowboy with his guns, perhaps out of step with his contemporaries, but they chose some pretty underpowered firearms in the process, that realistically probably wouldn't be used nowadays, given the available options, in my opinion.