It is, spurs too. They have "spur ride" events to earn those, and after a deployment with a cavalry unit you can wear gold ones.
It's also worth noting that the Hardcase is almost certainly a reference to Ted Nugent, so it's less about him being a literal cowboy and more him being an irregular trooper who thinks cowboy hats are cool.
Ted Nugent was known for busting out his bow and shooting flaming arrows at things at shows, or just for fun I guess. He also dressed a lot like the Hardcase with the vest and cowboy hat.
I don't think either of these are particularly convincing. The hardcase is wearing the standard USARF uniform with a bow and cowboy hat. There are a lot of bow hunters with cowboy hats in the US.
For the record, the Hardcase isn't intentionally based on Ted Nugent as the concept designer didn't know who Ted Nugent was until after the sculpt was shown...
Not like there are literally cable channels and entire chains of stores bigger than some towns devoted to them either...