I second Table Rock, just off the AT eastbound out of Grafton Notch as reasonable, probably broken and has a modestly steep but short stretch before the rock itself. Nice views.
As King Tut says, don't take the first trail, which is near the road, because that can be challenging in winter. I'd estimate that it's a lot closer to 2 miles than 4 round trip.
There is also a fairly easy hike with a loop potential at Mt. Will, on rt. 2/26 just before the intersection where rt. 26 turns off towards Grafton Notch. I recall there being a landfill on the opposite side of the road near the trailhead. It, too, gets steep just before the ridge but it's not bad ... I took my parents there a few years ago and they were in their early 80's at the time. The trail was well marked but doesn't get a lot of winter use.