Winter is my absolute favorite time to run. I actually run indoors for most of the summer, and then pop back out in the fall because of it! Winter runing is actually safer then runing in the heat, but there are still some precations you should take just make sure you stay safe and adjust for the changes cool whether brings! And don't run in temps below -15 (just in case...uhhh... you were thinking of doing that)
1. Seriously consider getting a "trail shoe", even if you aren't runing on trails because it will give you better traction against slippery ice. Or, if your short on dough, you can modify a pair by putting on sheet metal screws into the bottom(3/8" work best) .
2. As a rule, it is better to be too over-dress then under-dress, but clothing that can be taken off, rolled easily up or down, or zippered is the best. Try not to have skin showing, so gloves, even real thin ones are usually a good bet-and you lose most of your heat through your head so try and find a comfy cap that will stay put, but out of your way.
3. Wear synthetic socks over heavier ones that may seem better during the winter. Heavy socks just make your shoes fit improperly which will lead to blisters and pain and decrease circulation!
4. Try runing on flatter surfaces because your muscels react slower to terrain changes in the winter and changing to often/fast can lead to sprains and strained muscels.
5. Winter also means it's usually darker out so, you know-run safe with reflectors, obnoxiously bright and unfashionable clothes, and try to stay in lit areas!
Have fun!