I have an older friend who road his bicycle to school in the winter. In those days they didn't do as much snow plowing as they do today. Don wrapped his bicycle wheels with rope. He used manila rope, a little more than 1/4" in diameter. This is in the day when people used tire chains on their cars for traction on ice and snow. Remember that the rope will be a problem if you bike has rim brakes. I haven't tried this yet, but I may some time just to see how it works.
What to wearThis will depend on what the temperature is like when you ride. Like other winter sports you will want to dress in layers. Make sure that your base layer is a wicking fiber. As a boy I didn't know about this. I can tell you from experience cotton will not keep you warm when it gets wet. Remember that you create your own windchill riding a bicycle.
Under your helmetHaving crashed at different times over the years, I don't ride without a helmet. The helmet doesn't provide much protection from the cold. Cycling helmets are replete with ventilation holes. When it gets cold I wear a balaclava. This requires some adjustment to the helmet chin strap. Balaclavas are available in wind resistant fibers, but mine isn't. I wear a wind resistant head band. This usually means taking a little padding out of my helmet.
Choosing a winter bicycle gloveI have tried many combinations including various liner gloves and even an over mitten. I received a pair of lobster style gloves for Christmas. They have been effective in keeping my hands warm in Northern Illinois winters. The advantage for a road rider is the ability to operate the brake levers from more than one position.
Keeping your feet warmRiding in the winter will require some steps to keep your feet warm. Recently I notice some bike shoes designed for winter riding. I have used shoe covers in the past. The ones I had were hard to put on an take off. They had to be removed to take your shoe off. As with other winter cycling clothing, be sure to wear wicking fibers. Wool is also a great material for winter socks. One problem you may find is that there isn't much room in a bicycle shoe for a heavier winter sock. Remember that typical cycling shoes are designed to keep your feet cool in the summer. If you aren't concerned about what other people think, you can make disposable (recyclable)covers from plastic shopping bags.
Eye protectionIn cool weather you may find that your eyes tend to water as you ride. A wrap around style will help. Use ski googles when it get cold. When it is cloudy I wear clear glasses. On sunny days you need sunglasses with appropriate UV blocking characteristics.
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