The mythos of the cowboy is what is enjoyed. A behind you can bounce a quarter off is nice but looks fade and personality is forever. The idea of a chivalry is nice; however, old fashion has a limit. Yes, a person who likes livestock, respects women and can put in an honest days work is a lovely idea. The problem is that its hard to find one that can also discuss and share view on books, movies, politics and religion. There is also a profound difference between ranch cowboys, summer cowboys and rodeo cowboys.
The fact is that the cowboy of modern romances is something that never truly existed much like Barbie is as much a male fantasy as anything else. My advice, don't try to be something you think women (or men) will like. Just be yourself its easier and quicker in the long run.