My ideal winter headgear would be a windproof headband with a peak. Forehead and ears get bastard cold when it gets below zero, peak keeps sun/wind/rain out the eyes and at night it shields your eyes from oncoming headlamp glare. Majority of my head always gets too hot under almost any cap.
I don't bother with winter caps anymore - instead this is part of my essential winter kit:
https://www.decathlon.co.uk/warm-headband-black-id_8562961.html