The reason why cowboys were portayed like a solitary, strapping white men lies on the fact that that cowboy was a late romantic creation. Essentially, he represented the ideal of freedom.
In this representation, we find a lot of symbolism. Not only that, it is clear that this invented cowboy is part of the rise of segregation anti-immigrant racism. The lanky, tall Aryan is born. Most cowboys were actually Mexican and Indian. It is fair to say that there were actually some white cowboys mainly from European origin. To boost the image of the white tall cowboy, movies played a major role.
