classic Doctor Who would have had the insight that Steven Moffatt had: place a cowboy hat on the Doctor, and play with Western-style conventions.
In honesty, it happened over 40 years ago, with the William Hartnell story The Gunfighters, which was recently rereleased on DVD. It's gotten a bad reputation as being one of the worst (if not the worst) Doctor Who stories ever written, produced, and dramatized.
Having just watched the DVD, I can say that its reputation is not well deserved - the story is not that bad. In fact, although I don't share the enthusiasm for it as, say, some members of Radio Free Skaro, I think it's pretty much an OK - if not exemplary - comedic effort.
It's best to think of The Gunfighters as the Doctor Who equivalent of Red Dwarf's "Gunmen of the Apocalypse": a show that uses many of the cliches of the Western to tell an entertaining story. Except for the annoying repetition of "The Last Chance Saloon", it's a very simple - almost simplistic - staging of a traditional Western story. It also moves as an OK pace, the performances are solid, and it's not a total train wreck....at worst, it's simply OK.
The highlight of this DVD, quite honestly, is the documentary "The End of the Line?", which discusses some of the production challenges in the second and third year of Doctor Who. I have to admit, I've never been much of a Hartnell fan, but only because the show really hadn't taken shape (in my view) until Troughton. However, what this documentary makes clear is that there were often challenges, but that Who began taking shape - behind the scenes, at least - much more quickly than most people would expect. (It also makes me wish there weren't missing episodes).
Much like the main story itself, the documentary on the Doctor Who: The Gunfighters DVD has given me the opportunity - and desire - to visit (and/or revisit) some of the stories in early Doctor Who.
If you're a lifelong fan, you should watch this; if you're a casual and/or new Who fan, you can easily wait awhile.