The main issues are gear and clothing. For bad weather winter cycling gear, Cycle-licious recommends the cheapest beater bike you can find that runs. Salt, grit and water are hard on components. Derailers and brakes stop working with ice buildup, which is why fixed-gear bikes are so popular in the winter.
If conditions are dry, your regular commute bike will work just fine. Be aware that things work differently in the cold -- plastic things get brittle and break, oil is less viscous, grease turns into glue, and elastomers on suspension forks aren't so elastic anymore.
Clothing is difficult because people have varying levels of comfort. I'm good to about 0°F (minus 20° C) in the winter with a fleece shirt and shell, ski gloves, wool socks, fleece pants and shell, and Goretex hiking boots. Others I know bundle up in overalls and full parka when winter cycling.
Hat and gloves are vitally important. I also have a full face mask, but I only need that in high winds or extreme cold. I climb mountains and snow ski, also, and the clothing for those activities works well for winter cycling -- I have some cycling-specific winter clothing but I haven't found that to be all that necessary.
As the weather cools I bring more winter cycling information here. I discuss winter cycling more on this winter cycling page. I also can't recommend IceBike enough when it comes to interactive discussion about winter cycling.
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