I live in VT, so obviously I'm going to say Vermont of course! It sounds like you are coming from outside the USA, so you need to know we do not have the efficient mass transit as I have experienced in Europe. I live in southern Vermont near Stratton and Bromley mtns. It takes me 4 hours to drive to midtown Manhatten, but I would suggest a train from Albany NY as driving in NYC is NOT fun (which is my favorite city in the world!). You do NOT need or want a car there.
Other great ski areas in VT are Killington and Stowe.
As for snowmobiling we have the VAST system (see link).
The 3rd week of Feb. is a vacation week here, so I would avoid that time as ticket prices are higher, the slopes are more crowed, as are the resturants and hotels.
Jan and Feb are quite cold, so bring your woolies. I would suggest the last week of Feb and 1st week of March, but that's just me.
I have been to the Lake Placid area in NY as another suggests, it is just beautiful there, but I haven't found much else to do there than snowboard and shop.
Hotels depend on which area you decide to settle in. Here in Manchester the Equinox Hotel is the largest and has the most onsite amenities, but it's not cheap. Many of my friends really like the manchester View.
Hope you have a great trip! We look forward to welcoming you!
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