Census data consistently demonstrates that western states were often more international, per capita, than many of their eastern counterparts. Of course, a "cowboy" could be far removed from the urban settlements where foreign immigrants often settled, but it was a fluid society, and it is reasonable to assume that even someone working on a remote ranch would have many opportunities to go to town and would in general encounter a great many foreigners.

In addition, the educational systems in western states were generally good, so I would expect that in general westerners were very aware of the rest of the world. I deal with some of these issues - immigration and education - in my book The Roar and the Silence: A History of Virginia City and the Comstock Lode (1998).