Is there anywhere around NY, MA, or VT where I could hike/snowshoe up a mountain and then ski down?

A lot of the major VT ski resorts are also peaks that are traversed by the Long Trail or side trails (Stratton, Bromley, Pico, Killington, Sugarbush, Stowe, Smugglers' Notch,and Jay Peak are all LT peaks.) Trails also lead up to the tops of Mt.Snow, Okemo, and Burke. Likewise many people have skied Big Jay, Camel's Hump and just about everything else in VT with a Green Mountain Club trail. You can also ski the backside of Magic Mountain on the old Timberline part of the resort.

http://www.greenmountainclub.org/

If that's not enough, visit http://www.nelsap.org/ and try out some of the old ski areas throughout New England.

As for New York...try The Adirondack Slide Guide by Drew Haas. It doesn't give detailed info, but has great winter pix of all the skiable slide areas in the High Peaks. For trail info get a map from the Adirondack Mountain Club. http://www.adk.org/

Snowshoes are good, but invest in some Alpine Touring skis, boots, and bindings as well as some climbing skis. Lots of people also use wide backcountry XC skis like the Karhu 10th Mountain or XCD ski or the Outbound line of skis from Fischer. (Saw a woman on Smuggs last year skiing up Madonna Peak with those.)

The real deal is Tuckerman's Ravine in New Hampshire. http://www.tuckerman.org/