Are you looking to ride for transportation or recreation? That time of the year the snow banks are pretty high on the sides of the roads. Plus, many of the locals wouldn't expect to see a cyclist on the road in the dead of winter. Not to say it isn't doable, just a few more hazards...
If you're looking for recreational riding try the Western Reserve Greenway that runs from Ashtabula to Warren.
http://www.traillink.com/trail/weste...-greenway.aspx
http://www.ashtabulacountymetroparks.org/trail.htm
Admittedly, its never been plowed the few times I've been on it in the winter, but you have the luxury of being the only one on the trail.