I hate wearing any kinds of hats, but like you Jim, if I'm out with the dog and it's raining or threatening rain, I'll wear a ball cap to keep the rain off my face. If I'm out camping and taking long hikes in the sun, I'll also wear it. I wear a wool knit hat on cold winter days, usually just a black or gray one, nothing fancy.
We have one of those hats similar to the one in the photo, left by my father-in-law. It's around somewhere but we never really wear it. We both have super warm winter parkas for snow blizzard conditions with hoods that are warm and protect the face too.