If you don't have a choice but to ride in the inclement weather, here are a few tips, other than the obvious: Be careful.
Dress in layers. Wear thermals under your clothing. If you have felt inserts for your boots, one pair of socks is probably fine, but if not, wear a normal pair and a thick pair. Wear an oversize sweat shirt and sweat pants over your regular clothes. Then, add a hoodie and a winter or leather jacket. If it's raining, add a rain slicker over everything, making sure you put the hood up before you put on your helmet.
Always wear a helmet in snowy weather, even if your state doesn't have a helmet law. Put the hood on the hoodie up, then put the helmet on. Use thick snowmobile gloves.
Now, you're good to go for riding in cold weather. You should stay quite warm. I used to ride to work on a bike in the Connecticut winters, and this kept me warm even after 25 miles. Granted, I looked pretty funny peeling off several layers, but I wasn't cold!
Tips for Your Bike
If you happen to hit a patch of ice or something slippery on the road, do not hit your brakes, especially your front brake. Let off the gas and try to keep the bike upright. As you slow down, you can gently tap the rear brake. This is especially a good idea if you have someone behind you and that person is clearly not paying attention.Always get the snow/salt/mud off your bike as soon as you can. The mixture plays hell on paint!
Keep your bike covered in the winter. I used to use a tarp since I didn't have a garage -- this was way back when I was in my early 20s. The tarp kept snow and ice off the bike, and kept it from rusting, too.
Always ride in the part of the lane where the tires for cars ride. The heat from the tires dissipates the ice much quicker than in the center of the road.
Most of all, stay safe and keep your bike safe during winter riding!