I got busted as a 12 year old for riding my motocross bike on the road. they said it was a motor vehicle, even though it couldn’t carry passengers etc.
And yeah, you can haul people around on a zamboni. I’ve gotten rides on them many times.
On public property or private? I didn’t think they could give you a ticket until you were actually on the road, does that mean if a drunk guy pulls his car into his garage he can get hit with a felony?