Maybe, maybe not. Depends on how cold it gets, as early December might be above freezing most of the day, or might be frigid, and will most likely be freezing at night.
I traveled through southern Ohio in late 2003 and temperatures were in the low 50's. When I came through the next year, the Lake Erie shore was in blizzard conditions, and my trip to southern Ohio took me through an area where all power had been knocked out by an ice storm, the only places where I could buy fuel were those running emergency generators. Since then, I've been avoiding winter trips through Ohio.
The Adventurer has much of the fresh water plumbing in heated areas, but maybe not all the waste plumbing gets enough heat, but that matters only when you need to dump. I know the limits of my own RV, and I would not take it to Ohio in December and expect to live in it. A place to park, with hookups, will not be easy to find. There are a few (like the one on the turnpike) but basically, the RVing season is over. You must plan to provide your own utilities, power and water, because finding hookups is a matter of chance.