LOL, nothing to make fun of as it is not a stupid question. There has actually been some debate over the true definition of "cowboy" on this board before. I am one of the people that are more strict in who I define as a "cowboy" because I consider it a title that carries a certain level of honor and should be earned.
IMHO, a cowboy is a perfect combination of a horseman, cattleman, and gentleman. He should understand and handle horses very well and the same goes for cattle. His horses are ones that I would be proud to throw my saddle on (and I'm pretty persnickety about the type of horses that I ride
) and he can handle cattle and get the job done without causing a stir, no matter what the job is. He's polite and treats women with the respect they deserve (not like a china doll and not like one of the boys, somewhere in between
). He's honorable and true to his word, always pays his debts, both money and moral, and he's proud to put in a good day's work.
Anyway, that's the short definition LOL.
As for your original question, you really don't have to "earn" your hat color, just buy what you want and what looks good on you.
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according to my most recent research on cowboy hat etiquette, "hats off" is only what you do for a friend, or when you enter a building. With the exception of hallways in public buildings and post offices. 
