The laws for snowmobiling in Ohio are covered under the Ohio Revised Code, Chapter 4519.
Please view this link for complete information. Here is a brief overview:
1. All snowmobiles, except those used soley in private property, must be registered and display a registration sticker.
2. Snowmobile in Ohio are considered Non-Title. A bill of sale is all that is typcially requred.
3. The cost for registration is $34.75 for 3 years, or 14.75 for one year.
4. Snowmobiles in operation must have (at minimum): one headlight, one tail light, adequate brakes, and a muffler emitting no more than 82db.
5. All snowmobiles must carry valid insurance.
For more information on registration, here is a link to the Ohio BMV