We pull the water (a hose runs right into the lake to feed water to a pump and from there to the sinks and shower) the weekend we close (usually late November).
Although we have been up there for Thanksgiving. Ate everything off paper/plastic and cooked the turkey in one of those huge tin foil tins. The walk after dinner (which the whole family went on) amongst the fallen leaves on a brisk November day was something I'll never forget.
It really depends on when it gets cold enough for the water in the pipes to freeze (not the lake). We have to flush/drain all the water from the pipes when it starts getting too cold. That's when we know the season is over.
We've also been up there in February for a couple of days (one night). Chopped a hole in the ice, carried five gallon buckets up to the cottage to flush the toilet, wash dishes (after the water was heated on the stove), and taken a very chilly sponge bath (now you know why we stayed only 1 night).
So ideally, having a place on an island is a 6-8 (at best) month season. Something to think of if you're thinking of buying island property. My dad starts getting "itchy" to be back at the lake right after the chaos of the holidays. And he's there the first weekend after "ice-out" to open her up again.
Although I do know a gentleman who lives on Bear Island year round. He must have a generator or something to heat water for bathing...unless he's just really smelly for 4-5 months.