1914 seems pretty late for the age of frontiersmen and the "wild West." But there were certainly cowboys who fought. In fact Lord Strathcona's Horse regiment was originally recruited in 1900 from exactly that population as well as members of the Northwest Mounted police, in order to fight in the Boer war. They definitely went on to fight in France and their actions included a cavalry charge against a superior force with machine guns-it was successful though the attacking force was half wiped out.

From the US side of the border there was a whole "Wild West Division" (https://www.google.ca/amp/s/www.reviewjournal.com/news/military/remembering-nevadas-wild-west-division-in-world-war-i/amp/).