Welcome to Winter riding,
I found a nice hat at the local ski/bike shop. Thanks to the popularity of helmets for skiing there is now no shortage of thin hats available.
I found a Turtle Fur cap for around $20. The top is thinner, and then the band that goes over the forehead and over the ears is thicker and "fuzzier." Within minutes of riding I am pushing out plenty of heat so I definitely don't need a thick hat. I have a helmet cover, but I only use it in heavy rain or super cold temps (single digits F).
I foudn last year that the biggest changes start to happen when you get into the single digits. Breathing becomes a real problem. The air is so cold that it starts to hurt the lungs. I now have a PSolar face mask that pre-heats the air I breath and therefore can take deep breaths at 2F and not have it cause problems. IF there is ANY moisture on any of you lines you'll eventually end up with a derailer that won't shift or brakes that won't operate. It happens every so often. A few hours in either my office of the garage is enough the get everything working again. It is definitely part of what makes Winter commuting a bit of an adventure.
Happy riding,
André