Well, you can have lots of fun if you don't ski (but not as much
).
As others have said, there are tons of great hikes, walks, drives you can do in the park. One particularly good one is to leave from Upper Hadlock Pond and go up one of the several trail variations that go over Bald, Parkman and Gilmore and then head to Sargent Mtn. Then you can head south, southeast over Penobscot and Cedar Swamp Mtns to return to your car. It sounds like a lot, but it isn't. Definitely have a map as the area is small, yet dowsed with trails so you can easily get confused on which way you are going.
Bring snowshoes and crampons: you could need either or both since almost anywhere you go you'll have some windblown above treeline stretches and some potentially powdered crags between bumps. Ice is more likely than deep powder but be prepared for either.
If you don't end up with time for much hiking, a simple drive on the Park Loop Rd (one lane is plowed) along the coastal section is spectacular. You can combine the drive with shorter hikes up the Beehive (steep with a bunch of icy spots) or Gorham Mtn (less steep but fun terrain and cave-like spots).
You can get a cheap, free map at the park or in several places around town but the one mentioned earlier and the AMC map are far superior. Stop in at Cadillac Mountain Sports and they'll have some good suggestions for you (duh!).
Have fun and wave on your way through Bangor...
Spencer