So we go to the Cape often during the winter. We like the National Seashore for sure - Sandwich has some really cool long stretches Sandy Neck comes to mind. But there is an area called Blue Hills west of Quincy that has tons of cool hiking potential - we hike the all the time. It is not the Cape though but good. We have done winter hikes but not the mountains up high but in the valleys like Greeley Pond Trail but used snow shoes. It gets trekked out so it generally is not necessary. There are other trails like it that might fit the bill in the White Mountains. Do not think that White Mounts means climbing a mountain. South of the White Mountains there are places like Mount Kearsage or Mount Cardigan that are cool as well and not so crazy