Robert Coburn started ranching in Montana in the 1870s. He started the Circle C Ranch in the 1880s, and a grandson, Walt Coburn, tells the story of the Ranch in "Pioneer Cattlemen in Montana, the Story of the Circle C Ranch." Some idea of the nationalities of the cowhands can be surmised from the lists and comments in the book. This may be the only (certainly one of the few) book by a rancher that discusses the cowhands.
The names are predominantly Irish, English and Scots. There were a couple of Swedes. Over 70 cowhands are listed by name. Notable are a few Indian names, and mention of the use of the half-breed sons of the squaw men and their wives, employed in all phases of ranch work. A few were valued long-term cowhands. Roy and Abe Long Knife, Assiniboian, are especially mentioned, also Jesse Iron Hand from the Fort Belknap reservation. No Blacks are mentioned.
Unusual for many cattle ranching operations was a large pool of sheep, with a Mexican, Frank Nuñez, in charge (using "Scotch collie" dogs as well as horses)- (border collies?). Several Indians and half-breeds assisted with the sheep.

(Difficult to get data. It proved easier when I was looking into the Hawai'ians employed by the Hudsons Bay Company in Canada, and acting as voyageurs on the long boat treks. Some employment records were kept by the Hawai'ian Government and the Bay).