If your pile coat isn't really thick you may need another layer. Pile isn't itchy and it dries fast. Some pile hats have chin straps which keep your hat on in sleep. A peeked hat that dries fast is nice for keeping your hair dry in warm storms and shaded from the sun in warmer weather. The peak will protect your shades somewhat from falling snow.
Mittens are warmer.
Lite weight gloves can be one set of liners under mitten shells so you have some dexterity if you take off the shells without baring your fingers. Medium weight wool or pile mitten liners can be all purpose cold liners. It could be a knit hat with the top cut off by a pair of scissors. Pull it down over your head and around your neck. It serves as a super scarf without every coming undone.