I run pretty warm on the bike, and the Difesa cap from Castelli has become a real favorite. It is thin and fits under the helmet like a regular cycling cap, but it blocks wind rain and snow, breathes well, and does not absorb much sweat. This isn't the hat for a rider who needs a lot of insulation, but for warm riders or higher output efforts in bad weather it is the best!
There is nothing worse than cold ears on those cold days. Sometimes you descend down through the mountains, everything else is warm, but your ears have never been colder. All you need is something to cover the top of your ears, then you would be good. This hat is perfect for that. It keeps your head warm without over heating, and it keeps the cold air off of your ears. It pairs well with a neck gator or buff. You can handle any temps with a combo like that. It is a necessary piece while riding in the cold.