You can ride all year round anywhere the snow is not too deep to pedal. In Boston that's most of the time. Lots of people in the forums do it. With an mtb and studded tires you can ride on any ice.
There is an annual bike race on the Iditarod trail in Alaska. It's better to ride outside than a trainer.
An MTB is a lot warmer than a road bike and the wide tires with studs make any surface rideable.
You will be in much better shape in the spring too. There's a good video on line of some guys riding on the Charles river ice a few years ago when it was very cold. That year I was riding on all the lakes down here in R.I.