In many ways, this is a complex question. It might be also asked "What is a true Westerner?" During my recent two month speaking tour about the Butterfield Overland Mail Company in Arizona, I would sometimes experience the "outsider syndrome" because I was originally from New York State. There is a certain irony in all of this as the original pioneers were all emigrants from someplace else. One of the points I make in my talks is that the Butterfield Overland Mail Company was in almost every way a New York State stage line. John Butterfield was from Utica, New York, as were all the original executives of the line. Even William Ormsby, correspondent for the New York Herald, commented that most of the stage drivers were from New York State. The 1860s census, taken during Butterfield's time, has sixteen of the forty entries on one page listed as being from New York State.
When a winter visitor from New York State drives along Arizona Interstate 8, I wonder if when they see the signs for Mohawk Valley that they realize that the valley and the Mohawk Mountains there were named after Mohawk in Upstate New York? They were named after the Butterfield Overland Mail Company stage station site of Mohawk that was located a few miles north of the road. Five of the twenty-six Butterfield stage stations in Arizona had names associated with New York State. They were Seneca, Oneida, Mohawk, Stanwix, and Kinyon's.
So, when someone visiting Arizona meets someone born there (although someone who has moved there would also qualify) he may define them as a "True Westerner." But if they want to find an original Westerner (excluding Indians) they should go back East and look up what happened to great-great uncle Ned who emigrated to the West.
Several years ago, out in Arizona, a tourist couple from the northeast--not sure what state--spotted what they decided was a 'true Westerner.' The guy certainly looked the part--boots, jeans, a yoked shirt, big hat, silver & turquoise bolo tie. As he later reported on his radio program, commentator Paul Harvey, from Chicago, had to disappoint them.
What we all think of as "cowboys" learned much of their trade from Californios; such as roping a wild critter at 50 ft. or more with a braided rawhide or hair rope.
And what about the west of Canada? The Calgary Stampede, cattle, coal and furs in what is now Alberta, Saskatchewan and BC. A. Mackenzie, traveling by land, reached the west coast of NA and left his mark at Bella Bella in 1898. Several areas of BC supplied a large part of the worlds gold, mostly by placer in the last part of the 19th centr. Two "Indian" wars in BC, two in other parts of Western Canada and several battles. Cattle rustling, range wars, (of course, the NWMP never allowed any shots to be fired. Right.) Cattle operations from a few hundred head to a hundred thousand.
This doesn't include all of the information I've gathered in my research for my novels, but you all get the idea. None of this took place in the south west; but it did take place in the west.