I don't own a Cat... I have a boat with training hulls... a trimaran.
Heating a trimaran is much simpler generally, since the interior is far smaller, as is the exposed exterior surface.
Clear or black shrink wrap can be a pretty good way to add heat to the boat. One of my friends did clear shrink wrap with black cloth laid down on the deck...and it adds a fair amount of heat and insulation—so it is definitely something to consider.
A lot of marinas don't allow winter liveaboards, so if you don't have slip with permission to liveaboard yet, get it first.
I wouldn't recommend using a propane heater that isn't vented. The amount of moisture it can introduce to the cabin is phenomenal and will leave a lot of things soaked as it condenses out against the ports, hull interior and such. Doing that is a good way to get a moldy/mildewed boat.
You need to heat the cabin at least to some degree. A cabin that is below 55-60˚ is risking hypothermia IMHO, even if you're bundled up. An electric blanket is one good way to reduce the need to heat so much at night, but you'd want the head at least heated to a reasonable temperature, since using it late at night when it is cold is not fun or safe.
Shrink film on the hatches can help some...but it is far better to add more insulation than that if you can. Don't forget that you really do need to keep the boat fairly well ventilated, even in the depth of winter as well. Any lockers should have vents or screens in the doors.
Not everyone hauls out for the winter. Webb Chiles and his wife lived aboard at Constitution Marina for several years, prior to buying, then selling their Charlestown condo. Now they're living in Chicago, but Hawke is down in NZ.