Most people drive their own or rental cars to New England's ski resorts (here are distances from Boston and distances from New York City to all the ski resorts, and here's a map), but there are other ways to reach the slopes.
MBTA Commuter Rail Trains
MBTA Commuter Rail trains on the Fitchburg Line run daily from Boston's North Station to Wachusett station (1-3/4 hours), from which shuttle buses run you the 6.5 miles (10.5 km) over to Wachusett Mountain Ski Resort (map, 12 minutes). More...
Concord Coach runs daily buses from Boston's Logan Airport and South Station Transportation Center to Lake Winnipesaukee (for Gunstock), and through the Mount Washington Valley to Conway and North Conway (for Attitash, Black Mountain, Cranmore, and Jackson); Pinkham Notch (for Wildcat). Another route takes you to Littleton (for Loon Mountain) and Franconia (for Cannon Mountain).
Dartmouth Coach, a division of Concord Coach, runs daily buses from Boston (Logan Airport and South Station Trtansportation Center) and New York City to Hanover NH, giving access to the Dartmouth Skiway.
From New York City
Dozens of non-stop buses connect New York City and Boston every day. More...
Amtrak's Vermonter train stops at Claremont NH, 17 miles (27 km) west of Mount Sunapee; at Windsor VT, eight miles (13 km) northeast of Ascutney; and at White River Junction VT, in New Hampshire's Upper Valley, 19 miles (31 km) southwest of the Dartmouth Skiway.
You may want to take a flight to Maine, but if not, Amtrak trains run from New York City to Boston's South Station, and Amtrak's Downeaster train runs from Boston's North Station to Portland and Brunswick ME.
Rental car is also a good way to reach any New England ski & snowbord resort: