There are quite a few livaboards around.
There are many at Emerald City, some at Jefferson Beach and there used to be some at Michigan Harbor, not sure if they are still there.
Also, up on the Clinton river, I think it's Markley Marine and maybe another.
Another good choice is the Detroit Yacht Club. I have a friend who lives full time down there on Belle Isle. He loves it and it's cheap.
There are also some down on Lake Erie but I don't know anything about them.
Jefferson Beach is talking about banning winter livaboard but we'll see, I'm skeptical they will do that.
Your biggest headaches will be condensation, toilet and fresh water.
For condensation you need to insulate the inside everywhere you can. Reflectix is the most talked about solution.
For toilet, most use the clubhouse bathroom with a pee bottle for emergency overnight use. Some have a porta john service come to pump out but that gets expensive.
Water has 2 options; haul jugs or run a hose from the clubhouse to fill the tank. Obviously, you'll need to be close to the clubhouse to do that.
Plan on transparent shrinkwrap to act as a greenhouse. Works well.
In your boat buying budget make sure to set aside at least 10% to 20% for updates. You will probably find 5 times as many projects to do as you think. Also, you need money for survey including haulout. State sales tax, first year dockage, first year insurance. Lots of up front costs.