Here are some basic tips:
Clothing:
It need not be expensive. You don't have to have Polypro unerwear and a Gortex running suit. I tend to wear a standard issue T-shirt or long sleeve shirt under a cheap Nylon running suit. Just by adding a hat and gloves, I can get by with this outfit down to 35 degrees F or so. From 35 to 25 degrees F, I just go to a single layer of polypro underwear under the nylon suit. Below 25 degrees, I put on more layers and might wear a scarf over my face. I rarely run outside if the temperature is below 20 degrees F, though I have run in 60 below with wind chill just to see if I could. 20 minutes into the run, I had to duck into some woods to get out of the wind. I don't advise it, but it can be done.
Wear Layers:
Polypro or warm layer next to skin
More layers as needed
Wind/
water resistant layer on the outside
Outer layer should have zippers so you can unzip to cool off or zip up to stay warm
Pay attention to neck and wrist areas, adjustable zippers at the neck and cuffs you can roll up will widen the temperature range at which your outfit is comfortable.
In general, several t-shirst, socks, shorts and one set of long johns and a cheap nylon running suit will get you by.
Add hat and gloves for colder temps
Scarf over the mouth is good for really low temps
Wind:
Run into the wind early on run and put it at your back on the return. It is better to have the wind at your back when you are tired. Also, sweat builds builds up while you run and for some reason it is a lot colder to have the wind hit the sweat on the front of your body then when it hits your back. If you run into the wind on the early part of the run then turn around, you will be a lot more comfortable.
Snow and ice:
There is no reason not to run in shallow snow if you are careful, infact, it can add resistance and novelty to the run. The danger is hidden obstructions, branches, curbs, holes, etc under the snow. Always run on paths and roads you are familiar with and slow down as necessary.
I tend to limit my runs to snow that is less than a foot deep though I have run in deeper snow for a few hundred yards in open fields just to try it out-very tiring.
Ice is another matter, avoid it.
Precipitation:
Snow is usually not a problem for you as a runner but lowers visibility for motorists. You may need sun glasses to keep snowflakes out of your eyesTry to stay on trails or well onto the shoulder of roads when it is snowing. Also, you can run in a blizzard if you want to (I have) but you had better know your route very well. If the snow fall gets so heavy that you start losing sight of landmarks, go home ASAP.
Rain is actually a lot more of a problem than snow at lower temperatures, especially below 40 degrees F, because hypothermia can set in very quickly. If you have a rain resistant running suit, you will be fine. Cloth sweats like you are issued in the Pipeline rapidly soak up
water and are not much good after about 30 minutes in the rain at 40 degreees F.
Freezing rain and sleet are treacherous because they combine all the bad stuff: poor visibility, poor traction, increased risk of hypothermia and are often accompanied by high winds. I used to run in freezing rain and sleet in college but I just don't do it anymore unless it comes on while I'm already running, then I usually cut the run short.
Visibility:
Winter weather often means restricted visibility due to fog, rain, snow, and hours of darkness in the early morning hours and late afternoon when most of us are free to train. Even the gray overcast and general bleakness of a winter's day can impede a motorist's ability to see a runner. If you can run at lunch time, do so. Visibility will be at its best and temps will be higher than in the morning. I advise wearing a reflective belt or vest such as those commonly issued at most bases. Many sporting goods stores sell small reflective armbands/legbands for a few bucks. Reflective gear can be a lifesaver in low vis situations, especially if you are running on roads. Bright colored jackets and sweats are good too.
In general, you can run in anything above 20 degrees (including wind chill) with a couple of layers of clothing and be fine.
Hope this helps. MC