The cold doesn't have to keep you from pedaling down the road, though it may if you lack the proper clothing. We certainly wouldn't recommend jaunting through traffic on your road bike in sub-zero temperatures in little else than pair of zebra print underwear, a la cultural icons of Austin or Portland. Even they are sure to wear base layers and mitts (zebra pattern optional) during such hostile temps.
Our friends at Pez Cycling broke down the proper gear one should don depending on the temperature. It's a good reference for those who wish to avoid the stationary bikes and keep in shape for the spring season.
Side note: Temperatures are in Celsius, so we recommend looking up a conversion or gaining a small understanding of how the rest of the world reads temperatures.
Base layer; short-sleeved jersey; shorts; racing mitts; socks
Add arm warmers
Add knee warmers or 3/4 length tights; swap for thicker socks; swap mitts for thin full-finger gloves
Swap knee warmers for leg warmers; add gilet
Swap warmers for full medium-weight tights, thicker full-finger gloves; add long-sleeved jersey; toe covers or over-socks; head-band
Swap to long-sleeved base layer; thin hat, add race-cape/packable water-proof for changeable conditions
Swap to full over-shoes or winter shoes; thicker hat
Swap for heavier-weight tights; lobster gloves or mittens
Add a second long-sleeved jersey; a midlayer sock
Add additional base-layer; knee warmers under tights
0°C and below
High-risk of ice on the road so consider an indoor session! (unless you are a hardy, well-equipped and highly-skilled resident of the Northern Hemisphere)