Occasionally you can get out in the winter on your mountain bike in Ohio. There are a few trails, like Mohican State Park, that drain really well and hold up generally well under wet conditions. However in Columbus the nearest trail system is Alum Creek State Park, which features two 6-mile trail systems. They're fairly simple, but have some cool features like lots of ladder bridges, stunts, and a couple 1-3' drops. Unfortunately the soil there is largely clay-based, which means it gets unrideable very quickly with just a bit of moisture.
In winter this problem is hugely exaggerated. You can ride the trails if they are frozen solid in the winter. Which of course means freezing your ass off in sub-zero temps, usually first thing in the morning. That's something I'll do on skis but rarely on a bike. On the nice days when the sun pops out and it warms into the 30's and 40's, the trail turns to soup. Trying to ride the trails in such nice weather is disgusting, cakes your tires with mud to the point you can't move, and it does massive damage to the trail tread. So the local organization, COMBO (Central Ohio Mountain Bike Organization) closes them down during such weather.
