I don't know about South Jersey. Here in the north, Hurricane Sandy revealed some interesting things that caused a lot of headaches for many marinas owners and towns.
There were a fair number of boat owners who never bothered to register their vessels. They'd just leave the old registration numbers on. My guess is that they also had no insurance. When these boats ended up in the fields, on roads, sitting on RR tracks or sunk in their slips, The owners just walked away and couldn't be traced. When the marina was able to track down the registration numbers through the DMV, it would turn up a previous owner.
leaving the marinas to dispose of the derelicts.
I'm not saying that you would do anything like that. But Marinas learned alot of lessons in Sandy. They want copies of registrations, licenses and insurance on file. before they even sign a contract with someone. This was something they always stated, but were often lax in following up on. No longer.
Many will tell you that they don't allow livaboards, If you have never been a customer, and they don't know you or haven't seen the boat. A fair number of NJ marinas are family owned, clubs or municipal marinas. Before most of them agree to liveaboards they'll want to know who you are. It's often about building relationships.
Living aboard in NJ in winter is a real challenge. I don't know anyone that keeps water on to the slip. So you have to lug it. If there are power outages, you'd want to have a generator handy for bilge pumps etc. You'd need a plan for maintaining heat for yourself, if not electrical, what? Docks and decks get snowed on and ice covered. Fall in the water in the middle of the night and you're a goner.
Learning how to sail would be a good start.
If you're not detered and have the money, I'd seriously look at Denise's boat. It's well built and well taken care of.
Good luck in your quest.