What you are asking I think is def illegal. Atvs are too though unless registered and insured if on public land and allowed there. Bet your lawn mower isn’t. On private you’re good Even than you’d need to be allowed to use it there. In my area of the state most lakes have an electric only rule. That includes augers, any sort of motor actually and thus you couldn’t use it even on private lakes.
My question though is this is posted in NJ section. There’s nowhere in my mind any sort of transport besides a jet sled is necessary. Why do you think you even need it?
I’d also like to say many lakes have springs, bigger thin/open areas. You won’t be checking anything on a mower. Every year snowmobiles go under and they’re moving like your mower wouldn’t be.
Imo it’s an all around not great idea