I have trouble even in not-so-cold temps (60 degrees and below) with my ears. I have issues with the insides of my ears where if cool air gets in there and then I work out and my body temp goes up, I have pain. I'm wondering what I can wear under my helmet that will cover my ears but allow my helmet to still fit. All my hats and ear wraps (I don't know what they're really called - the bands that go around the head and cover the ears but leave the top open) are too bulky. Do winter cycling hats cover the ears or just the part of the head that goes under the helmet?