I think Delete has it pretty correct. Westerns and the old "Cowboys and Indians" games are not currently popular (and Cowboy's and Indians's is politically and ethically inappropriate) in today's society. I grew up with horses and lived in Texas during the Urban Cowboy fad of the 1980s. LOTS of people claiming to be big cowboys then, but it faded away. "Big hat, no cattle" we used to call them. In some Texas bars there were areas where they sent the "drugstore cowboys" while the regulars were dancing (Texas Tea House for one).
As a kid, I was all over my father to learn about horses. I spent hours looking at my Dad's books on horse husbandry, paging through Western Horseman, dragging empty halters around the yard, having a rodeo on a saddle stand, etc. This then evolved into working more and more with the horses. By high school, one of my best
dates was taking a girlfriend to ride horses. Spending a day in the saddle and being together.
Today, I can't seem to get my 13 year old boy interested at all. He likes girls, and I keep trying to sell the "most riders are girls and you can meet them on horseback...". I keep trying to figure out ways to get him involved, but he would rather sit on a bench playing with his DS while I work horses than be involved in handling the stock.
I think the instant gratification of video gaming has also taken away from riding for males. It takes a lot of hard work to set a good foundation and make a good horse and rider, and (IMHO) most kids today aren't interested in making the investment to really develop that relationship. They can grab a copy of Halo and be playing online with their friends within the hour.
I will also, at the risk of appearing chauvanistic, offer what I think contributes. When I was a kid, you just got on a horse and learned to ride from your parents. Most people I knew and grew up with never had a formal lesson, or saw a professional trainer work a horse (my Dad was our trainer). If a person was in training, they were typically female. Boys rode, or did rodeo, or roped, etc.; but didnt' spend time riding the long oval. Today, most parents don't have the experience or time to really spend with their kids teaching them horsemanship (I mean this for the 'general' public, not the people on this Forum). They put their kids into classes. At those classes it's mostly english (ok, probably an over generalization, but bear with me), and you're in tights and high boots, with a helmet. Not really the image of the Marlboro Cowboy riding the range.
Coming from the very Urban Southern California area, I see it in my rural neighborhood. Kids from the urban environment are taking classes, riding jumps, dressage, arena work, WP. The kids in our neighborhood, who grew up with horses, spend hours just sitting on the horse, taking them up and down the road, "playing" on and with them. The kids that will ultimately probably enjoy a lifetime of being with horses are those who grew up around them. The "schooled" kids will have it on their resume of things they did growing up like Soccer, Little League, Football, band, etc. But they won't grow up and start owning horses (for the most part).