Slop.

Real cowboys have big black and white spots, anything else is just a rancher.

(I've heard the same thing you did, but I don't have an actual source or anything, so have a cow joke.)

I think the detail is a majority were not white, many being black, First Nations or Mexican. Though White Cowboys were possibly a plurality in places

But most cowboy/outlaw stuff is just made up/exaggerated from books and films. Like a shopkeeper was more likely to have a revolver than a cowboy, because you want a rifle or shotgun when in the middle of nowhere.

black or latino, i'd expect. surely there were escaped slaves and also, as a free black man, maybe you'd feel more at home out west than among the densely packed crackers

I also read that so I think yes with the caveat that the conception of "cowboy" as some sort of gun-slinging mercenary or hero is a romanticized notion as part of revisionist history pushed by for example Hollywood. I'm sure there were gun-slinging black cowboys and Mexican ones as well. But most of them weren't getting into Magnificent Seven or John Wayne or Randolph Scott stuff. They were just herding cattle and doing other farm stuff and fending off the occasional problem but not riding rough to genocide Indians or spending their time taking down outlaws or avenge their kin in a blood feud.