Open carry is also legal in Ohio, but you won't catch me doing it without a lawyer on retainer and on speed dial. Again, WAY easier to simply toss everything in the trunk and be done.
So long as you aren't doing anything stupid, like leaving a loaded gun within reach, you shouldn't have anything to worry about. I've transported guns in various ways without caring at all, but I have a range bag so I put everything in there. I just sometimes forget to unload them.
Or you can get a CCW and not have anything to worry about. I can toss my loaded gun anywhere I want to so long as its not in plain sight, and I'm legal.