Its still doable even at those temperatures - here is what I do (though I don't use the bike when its snowing, yet):

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.