1. Dress well. Its especially important to fully cover your face (except eyes), ears and hands. Winter hat, scarf, gloves are always mandatory.
Legs may also need good (multi-layered) coverage but its not that critical. The number of layers for the rest of the body varies with the temperature
2. Don't overexert yourself. Avoid getting to a point where you're breathing too quickly or too deeply - this can be painful and can trigger breathing problems. If your breathing starts getting deeper and faster, slow down.
Basically, its much better to overdress and go slower than to under-dress and try to go fast to compensate with body-heat. Most cyclists will claim the contrary, but the contrary only applies after having some experience (or for people who just can't bear to go slow).
3. Carry extra layers of clothes with you. You never know if the layers you need in the morning will be the same as the layers you need in the afternoon.
Once it snows, I consider it far too dangerous (though again, there are a few people here that bike in snow w/ studded tires). I only have a bike lane for a short part of my ride, the rest being on 50, 60, and 80kmh roads with no paved shoulder. I don't want to find out what happens if I hit a deep patch of snow, ice, or some cross-winds while a semi is passing me doing 80kmh.
As for your 2nd point, I made that mistake the first time it got close to freezing. By the time I made it to work, I had a tough time breathing.
In my experience you don't want to be using a bike lane after heavy snow anyhow; they often don't get plowed. If you can take residential roads you're pretty safe (and studded tires really do make a HUGE difference).
But yeah, you don't want to be on the road with cars going 80km/h - I wouldn't be comfortable doing that every day in the summer, either.