Long ago, in my Jerusalem yeshiva days, I used to wear a fedora (a Borsalino, of course) — a brown one during the week, and a black one on Shabbos and Chagim (yes, with a bekishe).
I believe that hats, like all clothing and “accessories” (fragrances included), reflect (consciously, or otherwise) whom we are. I’m no longer that “yeshiva bochur“, that “kollel yungeman” or “ba’al habayit”, so wearing a fedora wouldn’t work for me, at any level, at all, anymore.
Sadly, I don’t have any photos from those days. Ex-wife (#2), an Israeli photographer, might have some; I’ll ask her, but we haven’t spoken in almost 20 years, so…