I live in Boulder, Colorado and ride year-round both for fun and fitness. It snows often, however, the roads are often free of snow.
I enjoy riding outdoors even when the temps are in the 20s. What do I wear? I start by consulting the thermometer outside my window and the weather forecast. I then select clothing based on the current conditions and then forecast high and hedge my bets in case the forecast is wrong. As a rule of thumb if I'm warm enough when I throw my leg over the top tube then I'm overdressed because I'll generate heat as I ride.
I pay particular attention to the forecast for wind. The breeze we generate while riding cools us in the summer, but chills us in the winter! Even with no wind, riding at 15 miles per hour at 40 degrees Fahrenheit the effective temperature is 32 degrees. To determine the wind chill consult the National Weather Service's Wind Chill Index.
Wind chill is one of the main causes of hypothermia, when your body loses heat faster than it can produce it and your core temperature starts to fall. Most cases of hypothermia occur when the temperature is around 40 degrees and it's unexpectedly rainy and windy.
Hypothermia begins with shivering and as your core temperature continues to drop, then your heart, nervous system and other organs don't work properly. If you lose fine motor control, for example you can't use your fingers to manipulate a zipper, or if you start to stagger, you are developing severe hypothermia and must get out of the cold.
More: 4 Winter Riding Tips
Loose Clothing is Good
Dry, still air provides the insulation we need. Although we choose tight streamlined clothing in the summer, in the winter looser clothing is better because it traps air for insulation.
Dress in Layers
Wear multiple layers, each with a different purpose, and to allow you to adjust your clothing as the ride (hopefully) warms up. On your torso start with a wicking layer to wick the sweat away from your body so that you stay dry. Do not wear cotton, which will stay damp rather than wicking away the sweat.
Then wear one or more loose insulating layers. If you expect conditions to warm up significantly, stuff a few layers of newspaper under your jersey as an additional wicking layer, which you can then throw away. Cover your layers with a wind- or rain-proof outer layer.