Welcome to the Discourse, Frammis.
I'm guessing that it's a deck of Congress cards - that back design would be something more likely to be found on the back of a two-deck bridge set. The deck has an Ace of Spades letter code on it - letter codes were introduced in 1904, after the days of the Old West were over.
I know only a little bit about Congress cards, but here's what I do know. The early decks had the Congress name on the Ace of Spades and came in both poker and bridge sizes. The later decks didn't have an Ace of Spades letter code because the faces started being printed by USPC before they printed the backs, allowing them some flexibility and saved time when the decided on what backs to use.
The AoS code alone indicates a number of possible manufacture dates: 1904, 1925, 1945, 1965, 1985 and 2005. I'm pretty sure that by 2005 (and possibly even 1985) Congress decks didn't have AoS codes anymore. A deck issued in 1904 would not only have the Congress name on it, I think, but wouldn't have that photo on the back printed in such great detail. Color photography itself didn't become popular and widespread until the development of Kodachrome film in 1935, but even by the 1960s, color photography was still expensive enough to the typical family to be reserved for special occasions.
Based on my observations and a little logic, I'd estimate that the deck was printed in either 1945 or 1965. I think 1965 is the more likely of the two - it's something about the style of the photography that leads me to think this, like a photo of this nature wouldn't have been typical of 1945 with the country still being at war and would have been considered outdated by 1985.
But bear in mind, there's only some facts in there combined with a lot of educated guessing - I could be completely and utterly wrong. Assuming it is a deck from 1965, I'd think the days of gunfighting were long over by then.