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......
John Lofgren Monkey Boots Shinki Horsebuttt - $1,136 The classic monkey boot silhouette in an incredibly rich Shinki russet horse leather.
Grant Stone Diesel Boot Dark Olive Chromexcel - $395 Goodyear welted, Horween Chromexcel, classic good looks.
Schott 568 Vandals Jacket - $1,250 The classic Perfecto motorcycle jacket, in a very special limited-edition Schott double rider style. 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...