Like Rick said, layering is key.  In Norther NJ where I am it gets pretty cold, especially last year, and I was able to run outside for about 95% of the winter (I only came inside to the TM when it was extremely icy which was like 5 or 6 days).  On the coldest days, what worked for me was (and i'm talking about teens and single digits) a tank, a long sleeve scoop neck wicking shirt, a 1/4 zip wicking shirt, a polor fleece 1/4 zip.  On the bottom, running pants under a pair of sweat pants and a headband and running gloves (not knit gloves but wicking gloves...make a difference as your hands do sweat too).  As the temperature rises, I lose layers startign with the polor fleece so.  For example, right now with temps in the 40's I'm still wearing compession shorts under my sweat pants, a tank, a 1/4 zip and gloves....usully lose the 1/4 zip and the gloves along the way.  You'll be able to monitor yourself once you get the layers going...be careful not to overheat.  It might be cold out but you will warm up, trust me.  Ice on the other hand is dangerous as I also run in the dark. I run with a light and usually right down the mddle of the street (early am).  if the ice is fresh, I'll stay inside but if the salters were out the day and the road isn't wet, I'll run outside.  Snow is usually no problem...I seem to have ok traction on fresh snow (there is nothing more beautiful than to run on fresh snow when the snow is still falling...its peaceful, quiet and gorgeous).  Be smart and safe and you'll be fine. 

Cyndi

Jennifer Anderson,

Actually, running tights don't need to be expensive.  My wife found a set of "warm wear" leggings at Target for around $8.  I found a pair of 80/20 polyester/spandex leggings (under the Starter label) at Wal-mart for $10.  I ran in the during our first major snowfall on Monday, and the leggings made a huge differnce in staying warm.  It was about 24ºF that morning, and I was running with baskeball shorts and the tights on the bottom, a similar tights-type long-sleeve shirt on top, and then another long-sleeve athletic shirt.  For warmth, I added a fleece vest, hat, and gloves.  Once it gets down near zero, I'll likely add some nylong windbreaker type pants that I can snap open on the side if they get too warm, and a windbreaker shell (I already used one on the cool days that were rainy).

You should get yourself some moisture-wicking next-to skin layers first. Don't wear cotton next to your skin because you will get sweaty and once it is wet and gets cold, you're done for. As long as you have one layer of the moisture-wicking you can wear cotton over that but definitely not too much. You should feel pretty cold when you first get outside but once you get going you will be warm enough in that, a llong sleeved T, and running jacket.

Cotton - bad.