If you're in Northeastern US right now, you're doing your best to stay warm. Last night I drove up to Killington to check on our house there, and the weather forecast for today was for high temps about -5! And windy!
So how do conditions like this impact your training? I've heard from countless people how running outside in temperatures cooler than 20 degrees can freeze your lungs! Well, that's just not so. The body has an incredible ability to warm the air before it gets to your lungs. While you do have to be prepared for cold conditions, there's no compelling reason why you're limited to the treadmill.
First thing, dress in layers. A good tech fabric shirt as the first layer will wick moisture from the skin. A mid layer to trap warm air is critical to being comfortable. Then, your outer layer should be a wind proof fabric. Wear two layers on your legs. A pair of tights against your skin will help manage moisture and a pair of wind proof pants will keep you legs warm. One pair of fairly heavy socks should be fine on your feet. The most crucial items of clothing will be gloves and a warm hat (like an old wool ski hat). If you can keep body heat from escaping through your head and extremities, you'll be surprised at how warm you'll stay.
Once you have your clothes laid, do a warm up routine before getting fully dressed. A very important element to running injury-free in cold weather is to keep your leg muscles warm. Starting out with increased circulations which results from a warm up routine will get you ahead of the curve. Cold muscles are much more likely to cramp or knot than muscles that are warm and supple.
Running is a huge limiter for me, but when I'm coaching on the mountain at Killington, I almost always run home from the locker room at the end of the day. And those runs where I'm generating a great head of steam on a very cold day are some of my favorite experiences. Enjoy the outdoors!