I don't know about this year, but in the past there have been couples who have stayed on Rattlesnake Island during the winter. I might be able to put you in touch with a couple of them if you're really interested. This is an adventure that's definitely not for the faint of heart.
I've heard that the wind can be relentless, and the wintertime conditions are very harsh at times.
My guess is the people who did stay on the Island are getting older and staying on the Island all the time is probably becoming more of a challenge because of the aging factor.
Isolation and "cabin fever" might be a problem unless you have a LOT to do (or are a newly minted couple

).
You would also need a very reliable source of alternate power, as the power has been known to go out (at least on Rattlesnake) for as long as a month in the winter.
The most practical solution would probably to get a not-too-expensive condo somewhere reasonably nearby (or make some other similar arrangement) - a place to stay if all else fails on the Island (like very bad conditions, etc.) and otherwise stay on the Island.
The same thought has crossed my mind, so you're not alone in these sorts of wild thoughts