Tires for mud, not for rock
Ohio publishes no traction or chain law, so tire choice here is a practical question rather than a legal one. The conditions that decide it are wet clay on a forest road in April, wet leaves in October and the long damp winter that ODOT spends plowing 43,000 lane miles of state, federal and interstate route.
Two things matter. A tread that clears mud instead of packing it, because reclaimed strip-mine ground turns to grease. And a tire you are willing to air down and drive slowly on, because the Wayne says some of its designated roads are passable only by high-clearance vehicles and none of them are worth rushing. Carry a full-size spare; services in Vinton, Monroe and Lawrence counties are thin.