I have a navy blue wool Swedish flat cap with concealed (fold-down) ear flaps for really cold days. It's made by Wigens and looks something like this:
http://www.delmonicohatter.com/Wigens-Caps/11008799.htm
Lock & Co where I bought it some years back now do this similar cap:
http://www.lockhatters.co.uk/Oslo-details.aspx