Ohio has a lot of great-undeveloped forestlands and ATV trails that make for some great riding. The winters are harsh in Ohio but the riding seasons for most ATV areas are from April through December and it's still a good, long riding season.
The State of Ohio does require that you license your ATV with the Department of Motor Vehicles in your area. The minimum age for riding an ATV in Ohio is 12 with a licensed and registered adult who is also riding an ATV. While it is not required, the State will give you a discount on your ATV registration if you complete a State approved ATV safety course. The State of Ohio also requires that your ATV be outfitted with headlights if you're going to be driving your ATV at night. You also must have a spark arrestor and noise muffler in place if you're going to be riding your ATV on any publicly owned lands.
Ohio has one National Forest that allows ATV riding but only on the designated paths. The Wayne National Forest has many miles of ATV trails and the riding season is from April through December. You must get a riding permit at the Ranger's office in order to ride your ATV on these trails.
Also if you're looking for some fun folks to ride your ATV with, you can check out the following groups at their websites : Ohio ATV Riders Association is the State's Official Group and you can see their website at https://www.geocities.com/oatvra. Another group worth checking out is the Far Mountain ATV Riders https://freewebs.com/farmountainatvriders.