I live in E Texas and would be more of the type someone might call all hat and no cattle. I wear a lot of fedora types, open roads, and large western hats. I grew up in N Louisiana and a lot of the older gentlemen at the time, late 50's to mid 60's I would see would wear normal suits, dress suits and a large western hat, No one thought anything about it, it was just common. I rarely wear boots, as I work mostly on my feet when working, but still wear my western type hats with whatever I want/Yeah, I do not own horses or cows, nor even know much about them. I feel that wearing a true Western hat is a lifestyle indicator, not just a hat. I feel that, in order to pull it off, you can't just have the hat. You must wear the pearl snap, the Wranglers, and cowboy boots, and let's not forget the belt buckle that can pick up 20 channels over the air. And, you need the truck to complete the look. When was the last time you saw someone wearing the outfit I just described, driving a Honda Civic?
I think the Open Road hat is certainly a nod to the Western US culture, but it's got enough fedora DNA to avoid being a true cowboy hat. I don't look at a guy wearing an Open Road and immediately think "movie extra from the set of Tombstone."
Bottom line wear what you like, and think nothing of it. It's what you like and care not what someone else might think.