Forty years ago, I discovered that a cowboy hat was great "climate control" outdoors. It shaded my eyes. Deflecting wind from my face was very helpful in cold weather. It also kept bugs away. However, it could blow off. It needed a cover in prolonged rain, and it got sweaty in hot weather. I'd wear a straw hat in summer, but a straw hat without a cord would blow off easily. The hats were a bit dangerous in that the broad brims could obscure a low beam as I approached.
A few years ago I supplemented my Stetson with a plastic cowboy hat. Weighing more than a pound, it stays put in wind. It's great in rain. It's a hard hat with a suspension, so I don't get hurt if I walk into a beam. In really cold weather, I can loosen the suspension and wear it over a knit cap. In hot weather, the airflow keeps my head dry.
For my first year on an ebike, I wore a helmet. Then I realized I was like American bicyclists in the 80 years before it was fashionable to bend over double and zip through traffic. I'd modified my bike for a more stable sitting position, I rarely exceeded 20 mph, I made myself as visible as possible, and I minimized interaction with traffic. In the old days, nobody wore a helmet because nobody got thrown headlong.
Two years ago, the plastic cowboy hat became my bike hat. Keeping wind, bugs, rain, and sun out of my eyes, it lets me see better, and the big white object way up high is very visible and identifiable. In winter, it's pretty warm even without a knit cap, by deflecting wind from my exposed face. It doesn't keep wind off my neck, so I wear a scarf.