The frozen prize of New England is the Black Dike, a 500-foot smear of ice that generally forms in November, about a thousand yards south of New Hampshire's state symbol: the Old Man of the Mountain formation on Cannon Cliffs.
If you're lucky, the wind will howl so hard your eyes will freeze shut - giving you a true alpine experience. This crystal granddaddy of icicles is rated Ice 4, not especially difficult by modern standards, but the setting often approximates big mountain alpine climbing at its best.
Dress for arctic conditions. New England ice is plentiful but temperatures often hover in the single digits, not to mention the wind chill. Avalanche danger shouldn't be discounted - so don't go climbing after a fresh snow.
For a mellower ice experience, try Willey's Slide in Crawford Notch (halfway between North Conway and Franconia, NH). It's a moderately sloped sheet of ice, 700 feet long, with an awesome summit. Call the EMS Climbing School (800-310-4504) for details about conditions and lessons.