I'd say adjust plans - check out North Conway or Lincoln, NH over the cape but skip the hiking if you dont know what you are doing, you need the right gear - microspikes, snowshoes, winter hiking clothes. North conway would be a good call. Enjoy the shops and food, drive around and hit some of the outdoor views like cathedral ledge, the kanc, drive up to Gorham and pull over to sightsee. Loop back around to Bretton Woods to look at Mount Washington via the Omni. Lots of fun stuff to do without putting yourself at risk.

The Cape is boring and lame - I'm a North Shore person who prefers NH so I have a bias :)