Well, if that's the timeframe you have to work with, then I'm not sure what question remains. Mid-October through January, isn't the answer really obvious? Go as early in October as you can, since the weather will only going to get worse with each passing day. Sure, you might luck out and get a unseasonably warm, sunny day in mid-January, but there's not any way to know that more than a day or two in advance, and it's a not a good bet. The usual advantages/disadvantages about winter travel in Europe apply, of course: shorter daylight, fewer crowds (except possibly around major holidays), cold/wet weather, possibly lower prices, possibly limited open hours for some attractions...etc.
If it were me, I'd just go on the earliest day in October that you possibly can, and I'd expect the chance of wet/cold weather to increase with each day of delay. Go prepared for cold and wet, because there's a good chance you'll get at least some of that, and hope the weather gives you a break at least some of the time.
As to the specifics: I'm not sure I'd spend two nights there. I think MSM is best done by arriving there in the afternoon (it'll probably still be crowded even in October), enjoy the place as the crowds drain away late afternoon and in the evening, spend the night on the Mont itself, then get up early, enjoy a few hours more, then get outta Dodge mid- to late-morning as the tour buses roll up.