This is a cross post from my Beginner Triathlete Mentor Group.
Take it easy.
Try to run when the sun is out. It will be slightly warmer, and easier to see ice/snow and for cars to see you/
There is no need to buy special things to clamp onto your shoes, simply take a pair that is close to being worn out and convert them yourself: http://www.skyrunner.com/screwshoe.htm
Wear brighter clothes, since sidewalks and the edge of the road may have snow/ice. You may find it easier to run in the road. Continue to run against traffic, but brighter clothes in theory should help drivers see you easier/sooner. Cars may also have a harder time stopping if it is slick out.
Wear extra clothing but not too much. Everyone is different when it comes to warmth and their ability to deal with the cold. Gloves and hats are essential to keeping warm. I also recommend Sunglasses to keep the wind and cold out of your eyes. For the men you could add something like Brooks Wind Briefs under your running shorts. Likewise if it is cold enough wear tights. A tight fitting warm technical top with a tshirt or long sleeve over it works great.
Run on trails. I love breaking new trails. Its a hard effort, but rewarding. The woods are quieter, you see more animals, its just nice.
If it is cold and very windy, run inside. Air is an insulator, wind removes that insulating layer of warm air around you. Your movement also creates wind chill because it increases air movement past your body.
Make sure you still keep your fluid/calorie intake up. You may not sweat as much, but the energy use / sweat is still there.
Run on a treadmill. The treadmill allows you to be more specific and more deliberate in your pacing. It is easier to do intervals or tempo run at different HR levels or paces.
Shorten your stride if it is icy. You will have more control and be able to better see where you are running. Be deliberate in where you step.
It may sound silly, but try to avoid ice.