Added some more tags. By the way, the English names for the HeartGold and SoulSilver protagonists (Ethan and Lyra) don't redirect to the Japanese names (Gold and Kotone) like the English names for all the other protagonists do.
Showing this to my thirteen-year-old sister, who's nowhere near the kind of fanatic we are, thought the new starters we were enough to merit vocalizing that sentiment when confirming the Balls' order.
I for some reason doubt that. When traveling the world, a good hat is a wise investment, since head cover can further protect you from the elements. First gen has eye-covering brims, good for keeping your eyes healthy against too much sun exposure. 2nd and 3rd gen, minus Lyra, I'm not too sure on their practicalities, though I suppose it keeps the hair out of their faces and can act as sweatbands. Dawn's is obviously to deal with the cold, when Lucas's may have both cold and light protection. 5th gen goes back to the simple sensibilities of a baseball cap.
Toho's gals, though, I doubt it's anything less than a fashion statement (except maybe for that kappa girl). They're otherwise beyond the threats of the mortal world.
I think you're over analyzing things, maybe Satoshi just likes his protagonist to wear hats. And there's no way Dawn's original outfit is meant for cold weather.