@Abe Cohen -No he does not. Anywhere. And even where he cites a double head covering as praiseworthy, a cap fits the bill just as well. That’s what the Chafetz Chaim (and most Polish and Lithuanian Jews of his times) wore on a daily basis.
It is worthwhile to point out that 50-100 years ago the fedoras worn were not necessarily black.
See the (in)famous pictures of the Bochurim in the Mir and Slabodka.
IMHO the black hat as a uniform is something that rubbed off on the Litvaks from the Chassidim.
And yes, I wear a black hat.