I'd say the best match would be the wool watch cap, second one down in the above photos. That way, you can pull the hood over your head for maximum warmth, which is why Id wear a jacket like that in the first place.
I wouldn't wear a fedora with that coat. Maybe something like......
You can't wear a fedora with a jacket like that? Oh, ohlol
You can't wear a fedora with a jacket like that? Oh, ohlol
What kind of hat is good with a brown Woolrich Artic Jacket (the short one).
I have a brown and a grey fedora but I think I look like too Indiana Jones...