Gearing Up
It is easy to be deterred from cold weather running if you don't have the right gear. But if you do have the right clothing, then winter running can be not only bearable but enjoyable. The typical rules for cold weather clothing still apply: wear lots of layers, avoid cotton and make sure to cover you head. But when you add in the aerobic activity factor of running it becomes a little harder to plan accordingly.
What you choose to wear is not just dependent on the outside temperature and potential wind chill, but also on the intensity of your run, the duration of your run and your own body temperature tendencies. If you're planning on a brief but intense run you may want to choose two or three lighter layers as your body temperature will rise quickly and lighter layers are easier to shed and tie around your waist. If you're going to be running for a while at an easy pace, then a combination of a light layer and thicker outer layer may be best since your body temperature will take a while to rise, but once it does it will be sustained.
Remember that clothing guidelines are not prescriptive, body temperature and cold tolerance is specific to each individual. My own body temperature seems to have drastically changed now that I am breastfeeding: I have become a furnace. Prior to pregnancy I was constantly cold and typically would need an extra layer to be comfortable doing anything outside in the winter. Now, I don't need that extra layer.
Here's a few examples of what I wear depending on the outside temperature:
20 degrees and below
If it is this cold then it is usually because of windchill, which means that you need to have an outer shell that blocks the wind. A windbreaker shell can work well, but if you're serious about running in the cold you may want to invest in a soft-shell windblocker jacket. I wear the New Balance NBx Windblocker Jacket, which I found at TJMaxx for a steal at $35 (most windblocker jackets are $70 and up). Under my windblocking layer I wear a heavy-weight, thermal long-sleeved shirt (Sugoi Speedstar Crewneck Top). On the bottom I wear a pair of fleece lined tights by Asics. On my feet are a pair of wicking socks that tuck into my tights and cover the ankle. And on my head a fleece cap that comes down over my ears and lightweight gloves.
20-30 degrees
My Asics tights are still a must in this temperature range. But my upper layer changes slightly, instead of a windblocking top I wear a simple fitness weight fleece jacket (LLBean Fitness Fleece) over a long-sleeved mid-weight thermal top (Champion-Target). The fleece top is more breathable than the windblocker top and combined with another top is enough to keep me warm. I usually switch to an ear-band instead of a hat and keep the gloves on. My ankles don't get quite as cold so I just wear my low cut running socks.
30-40 degrees
If it is this warm (such a relative term, in my Arizona life I this would be as cold as it gets) then I usually wear my lighter-weight running tights, a simple lycra tight by Nike. I'll switch to a short-sleeve top under the fleece jacket. I keep the ear-band and gloves, but often get rid of these about 3/4 into the run as I start to warm up.
Winter running gear can often be rather expensive, so I often shop TJMaxx, Target and outlet stores, where you can often get gear for discounted prices. Having the right clothing can certainly help make your run more comfortable and even motivate you to get out the door. Hey, if you're going to get out there and run, you may as well look good doing it!