Kube, unless you were a child prodigy (which you probably were), I would put you as being born ca. '48-'50. The standard following question about a cowboy is "What was his horse's name?" I don't know about this, because "Can a cowboy who is a horse have a horse?"
Probably not. He did have a side-kick named "Baba-Louie" or some such, who I seem to remember as being a Burro.
"Quick Draw" was a step down from Huckleberry Hound", in my opinion.