To get to the mountain follow the Appalachain Trail! Katahdin is just north of Millinocket, ME, in Baxter State Park. There are detailed directions and insructions for winter climbing on the state park web site: http://www.baxterstateparkauthority.com/ The park is awesome in the winter and offers full bore, hard alpine climbing as well as shorter, more friendly ice climbs. Expect to spend two days coming in and out as you are required to stay at the Roaring Brook Campground on your first and last night in the park.
The Classics
Mountain Project's determination of some of the classic, most popular, highest rated routes for Katahdin:
Cilley-Barber WI4 Trad, Ice, 7 pitches, 1000 feet, Grade IV
The Armadillo has just about everything you could hope for in an alpine climb: Chimney climbing, face climbing, crack climbing, ridge climbing, big time exposure, solitude on the route mixed with gawking, awed filled hikers at the top. This route climbs at least 6 pitches of the huge pyramid and ridge in the middle of the south basin to the rim of the mountain, 10 minutes from Baxter Peak. Expect to get an early start and plan for a long day. ...[more]Browse More Classics in ME
In the summer the park rangers will hand out a "Technical Rock Climbing At Katahdin" paper which has general information (basic route descriptions with grades that are not all that helpful.) There is also an informal guide book with photographs and drawn lines of the routes along with descriptions from many of the first ascentionist. Be prepared to show your gear and lay out your intentions to the ranger on duty, who may or may not know something about climbing and may or may not be polite and respectful.