I leave it outside, under cover, sandwiched between our cars and the house, chained up, hooked up to a battery tender, with a surveillance camera over top, and a 12-guage 4 feet away.
I'd like to hope I live in a decent neighborhood to where I don't need to worry about it, but you never know. It's a pain in the ass getting the bike out, I need to move all the damn cars every time. But I'm a little paranoid after having mine and my wife's dirtbikes jacked from my step dad's barn recently.
Anyway, to the OP, as far as any corrosion or anything from leaving it outside under cover over the winter--I haven't noticed anything.