I love the North Conway area in NH. It might be a bit over your 4 hour limit seeing as how you are in Long Island. I know it takes us about 4 hours to get there from where we are, but we do take a bit more of an indirect route instead of just shooting straight up 95.
Attitash Mountain has snowmobile rentals along with snowboarding. They also have outdoor concerts and lots of other fun things to do.
Just down the road in North Conway itself is Mt Cranmore. They do snow tubing there along with snowboarding. There are places within town where you could rent snowmobiles.
Bretton Woods is a beautiful resort. Reminds me of the hotel from The Shining.

They have snowtubing, snowmobile rentals, snowboarding and the list goes on. Here is their site.
http://www.brettonwoods.com/
I think Loon Mountain does snowtubing also. Not sure though, as I have never been there.
Lots of other stuff to do in the area including outlet shopping, hiking, great restaurants and it is a very family orientated area.