The right gear gets me to around 20-25 F. I can run at colder temperatures, but it's kind of miserable. Other people handle it better. You also need to worry about timing (in December-January, if you run at 4:00 PM, it could be dark by the time you get back; aim to run at 3:00 PM). Traction is also an issue - traction aids will work on ice for maybe 4 miles, and fresh snow isn't too bad if it isn't deep, but fresh snow on top of ice is bad. Make sure to add some lighting or reflective material if you run in the dark.
Find an indoor track. It can be boring, but it beats running outside at 0 F or in the dark on icy roads.
Use a treadmill. It's even more boring, but maybe you can set up a TV to watch or something?
Get a spin bike. It's even more boring than a treadmill, but you can buy one for your apartment for $400 or less. Also, 5 minutes biking makes a great warm-up before going outside to run.
Basic kit: running pants over running shorts, long sleeve shirts (add an extra as it gets colder), running jacket, gloves, thin head covering.
Extra credit (down to 0 F): tights as 2nd leg layer, balaclava/fleece cap, fleece mittens