You're fine! Funny, but when we wear our cowboy hats, seems like everyone we talk to asks us, "you from Texas"? Like Texas is the only state where folks wear cowboy hats. It can be hard to know what I'd say to the "howdy cowboy" statement. Possibly it can depend on what the person is wearing. IOW, wearing normal western attire (nothing flashy) and a rodeo trophy buckle, I'd feel good about it. I've never had it happen to me, the "howdy cowboy" thing. However, when wife and I were at Bellagio Hotel/Casino, right before Christmas, to see their Christmas decorated room, she got three great comments about her black felt cowboy hat and western attire.
Most folks can tell the difference between "big city" folks and current or former rodeo/farm/ranch folks. However, during the summer months, wife and I are in shorts, tennis or walking shoes and a short-sleeve shirt. If we decide to go out to dinner in western attire, we will do that. What I already knew, from my years in professional rodeo before meeting my wife, and what both wife and I have notice during our 24 years of marriage, rodeo/farm/ranch folks can be, and most likely are, much friendlier than other folks. But, that's what we've encountered at many rodeos or other "western" related events we've been to or fans of rodeo/western lifestyle we've met.