It's always weather dependent. Snow shuts you down unless you're really hardcore, a mt. bike, or cross bike with good knobbies works on snow covered streets, but not on black ice, which is a huge concern. You can mt. bike the trails, it's always better when the trail is frozen but snow free anyway.
Invest in clothing for cold temp's and this includes booties to keep you feet warm if you use cycling shoes and clipless pedals, plus a wind proof layer if it's windy. etc... My limit on the road bike is about 25, then I'm in the woods on the mt. bike.
You can also invest in lights, good LED head and bar lamps. They work very well and let you do the trails at night, or the North County Trail (just watch that black ice). Or with an extra set of white and red blinkies, ride the roads.
In truth though, I don't ride as much in the winter, living on Long Island. Typically mt. biking at Bethpage, unless it's wet or muddy, or road if the temps are above 35. I do other activities, swimming, indoor cycle at the recreation center, drink beer, etc... It really comes down to your tolerance level.