The choice of the Walker Colt to arm Josey Wales was really my only complaint about the movie. In the book on which it's based "Gone to Texas," the author simply calls them "Colt .44s" and almost certainly intended them to be the 1860 army model. Which would make perfect sense. Leaving aside the unlikelihood that Josey would have found not one, but two revolvers that had been out of production for twenty years, and never numerous to start with, they really are impractical for belt carry. Moreover, Josey is supposed to be lightning fast as a pistoleer, and the Walker would by just about the worst choice imaginable for someone who wanted to execute a fast draw -- not just the weight, but the extreme length of the guns would be working hard against you. It's a classic case of Hollywood excess: the hero has to have the biggest, most badass gun out there. You can see this attitude today with action heroes in some movies carrying big Desert Eagles and so forth (though thankfully they seem to be getting away from that a bit nowadays).
As others have remarked, the Walker was never intended for belt carry. It was a horse pistol. Not only were very large "horse pistols" common for military use in the era of single shot muzzle loading arms, when Samuel Colt marketed the Patterson, and it proved such a hit with the Texas rangers, he no doubt had an eye toward more such sales, and he was taking the advice of Texas ranger captain and Republic of Texas army soldier Samuel Walker. When the revolver debuted, it was a handgun that offered more firepower than any previous arm practical for military use. But there was no comparable longarm that gave the individual so much firepower. I think what Walker wanted, for the cavalry and for the Texas rangers was the best of both worlds. He wanted a repeating firearm with more range and power than was typical for a pistol. There were no long guns on the market in the 1840s that gave any shooter this kind of firepower, so he and Colt collaborated to upscale a revolving pistol so it could fill the role. Then came the Dragoon models -- slightly smaller, but still definitely horse pistols -- when the Walker proved a little too powerful (there were a number of kabooms). But note that when practical repeating long guns like the Henry and Spencer rifles came along, no one ever made these big horse pistols again.
