You might investigate the Taconic “Alps” ;) eastern NY, western Ct and SW Mass tri-state area. Lower elevations and easy to back out if the weather gets dicey. Also has some stretches above “treeline” Nice sweeping views. Plus the AT goes through this area. It’s a good bet for winter and actually really good fun. I’ve done a lot of day hikes in this area while visiting the in-laws for Christmas and didn’t have any difficult conditions.
Not sure about the camping but there’s bound to be some. The folks on the AT are camping somewhere. A note of caution we did see a cabin near the summit of Bear Mt or it might have been Brace Mt. It was REALLY rough looking. I’d check carefully for reports on the campsites and any trail system cabins. Get up to date info and check for reviews.
This thread currently on page 2 is the same general area: Harriman State Park