Even though it's cold outside you can still go outside and jog, run or just take a good walk.
When going outside for a walk, jog or to go running in the cold weather just be sure to dress warmly and wear a scarf, earmuffs, gloves and even a scarf over your mouth.
As long as you're dressed appropriately for the cold weather then you'll be able to keep your body heat where it belongs to keep you warm.
You also lose a lot of heat through your head so be sure to wear a good stocking hat on your head to keep your head warm.
Then once dressed up appropriately you can still head outside for 30 minutes to an hour for a good walk, jog, run or even to ride your bicycle to stay active.
I still go outside when I can to jog or walk or even ride my bicycle and I stay fit and healthy throughout the winter months.
You can also setup a home gym and use a treadmill, exercise bike or go to a gym to stay active and fit during the cold weather.