In it's earliest days the western genre WAS simply adventure. The genre's roots were in the 1880s (maybe the '70s) and while it took place in areas that were depopulated enough so that they could be considered exotic compared to the "east," there were certainly many western readers.

The clearest example of the breaking up of the adventure genre into the Western, Historical, and Science Fiction sub groups we see today is the work of Edgar Rice Burroughs. He write in all three categories, occasionally cross pollinating them significantly ... and why not I'm guessing that to him it was all the same thing.

A Princess of Mars takes a soldier in the cavalry in Arizona (I think I've got this right) to Mars, which incidentally looks a lot like the northern AZ desert! ERB actually served with the 7th Cavalry out of Ft. Grant AZ in the 1890s.

The Mad King takes the son of a wealthy mid western farming family to a fictional Balken Kingdom and into a "Historical" seeming plot similar to Prisoner of Zenda ... and then brings him back on the eve of WWI, just after the assassination of Franz Ferdinand.

The Mucker is a classic Far Eastern adventure but the "hero" is a gangster. Return of the Mucker is a Western set south in the border in a situation much like The Wild Bunch.

The Bandit of Hell's Bend, The War Chief, Apache Devil, The Deputy Sheriff of Comanche County and even The Girl From Hollywood are all somewhat classic Westerns.

There's a lot more detail to ERB's genre mash ups ... except they weren't really mash ups. He was writing between 1914 and 1941 (after which he became the USA's oldest war correspondent!) and he mostly just wrote about the times he lived in. Very little of his work was set in the future and only slightly more of it was set in the past.