According to a Lubavitcher rabbi I know, Menachem Mendel Schneerson, before he became 7th Rebbe, wore a gray fedora and wanted to continue to do so after he became Rebbe, but other senior rabbis convinced him to switch to a black fedora.
As for exact size of fedora, see photos from 40 years ago – hats were much smaller. And, of course, Moses’ fedora ….