I thought it was always open - there are houses right across the street from the trailhead.
You'll like the Doubleheads. Great views of the North Conway area, just be sure to fully explore the trails around South Doublehead's summit. There are some nice ledges and viewpoints in every direction. It isn't a long hike, though... I did them both in December and it took me 45 minutes total, mainly because I ran down the ski slope in my snowshoes! So much fun!
Another nice (short) hike to do if you have extra time while you're up there is Iron Mountain in Jackson. And I believe it is on the 52WAV list...