In a survival situation you want to be as efficient as possible with regards to maintaining and regulating your body temperature, lost in cooler or windy environments.
A wool hat, beanie, or touque (in Canada) is your best solution to stay warm in this situation. It also covers up and manages your (long) hair, if you’re having a bad hair day.
Additionally, wool does not absorb odors, so you can wear the hat for extended periods of time.
Alternatively, you can use a neck-tube, or a merino wool Buff, or as a last ditch alternative — a cotton bandana.
This type of head cover should be considered a part of your cover or shelter system.