Running and cycling shops, as well as a lot of other places, have a variety of caps, headbands and beanies in a variety of weights that will work under a regular cycling helmet. Some are designed to cover your ears, forehead and the back of your head (occipital region). When it gets colder you can switch to a balcava or add a facemask in addition to a skullcap. I found a heavy balcava that has an extra long neck section with a light elastic cord in the hem. In really cold weather, the neck section can be cuffed inside of itself so that the hem ends up over the nose and mouth and you get a double layer of fabric over the neck. It is still long enough to tuck into a high necked winter jersey or jacket. I wore this with a jacket that had a hood big enough to go over my helmet and rode to -14 degrees F last winter (see avatar). If you want to ride when it's really cold, you can get a ski helmet and goggles. Ski helmets are designed for speeds and hazards very similar to what are encountered in cycling and the impact standards are almost identical.