The first is pure common sense. If your brain tells you not to ride, you probably shouldn't. Dedication is important, but winter weather can produce very hazardous conditions. Snow and ice can be treacherous not only for you, but also for drivers around you. The cars crawling past you at 35 miles an hour may seem to be driving carefully, but they're one patch of black ice away from losing control. Even after the snow melts, sand patches can pose a serious threat to cyclists. If it seems too dangerous to ride, it probably is. Take the opportunity to do some cross training - hit the weights, run on a treadmill, set up rollers or trainer.
The boy scout motto of "Be Prepared" is great advice for anyone braving cold weather. The old test of stepping outside before deciding what to wear doesn't always hold water. Take into account the fact that you're going to be moving quickly through cold air and dress accordingly. It is always better to dress warmly and peel off a layer or two than to go out underdressed.
Which brings me to another tip - layers are vital for any cold weather athletic activity. It may be cumbersome to don several light layers, but it's vital for comfort. The weather will likely not be the same in the morning as it is in the afternoon. Once you're body is warmed up mid-ride you will probably not want to be wearing the same clothes as you were when you first set out. Layers allow you to quickly adapt to changing weather and ride conditions and stay comfortable no matter what mother nature throws at you. A comfortable rider is a strong rider.
But there's no sense in layering sweats and polo shirts - invest in quality clothing. My winter wardrobe consists of arm warmers, leg or knee warmers, baselayer, bibs, jersey wind vest, skull cap, and shoe covers. Sounds like a lot, but as mentioned above as the temperatures start rising, it's easy to shed any of these layers and stuff them in a jersey pocket. If you have the option to buy windproof clothing, such as warmers or bibs, it is a worthwhile upgrade. Modern technical fabrics do a great job of wicking sweat away from your body, keeping you dry and warm.
As you ride and start warming up you might be tempted to start shedding layers, but you might want to reconsider. Remember that warm muscles perform better than cold ones. The old rule I adhere to is that if the temperature is below 67 Fahrenheit, it's worth wearing arm and knee warmers. This goes double for the extremities since the body tends to sacrifice blood supply to the hands and feet to keep the core warm. Shoe covers are a very helpful accessory and a thin pair of gloves can really help keep your fingers comfortable. Of course this all depends on your cold tolerance. As a transplanted Texan, mine is quite low.
Those are my basic clothing strategies which have sheltered me through a bitter winter. Hopefully they can help you brave the cold out on your early spring training rides.