You can do a loop to Clingmans starting at the Deep Creek TH, but I'll also give a good suggestion from the end of Road to Nowhere which is a few miles from downtown Bryson City.
Deep Creek TH --> Deep Creek Trail --> Fork Ridge Trail --> AT --> Clingmans --> little bit of road (which will be closed to traffic) --> Noland Divide Trail --> Deep Creek TH
I don't have a trail map in front of me, but that loop is probably about 32 miles.
Start at the tunnel at the end of Road to Nowhere (aka Lakeview Dr / Fontana Rd) --> Lakeview Trail --> Whiteoak Branch --> Springhouse Branch --> Forney Ridge --> Clingmans --> Forney Creek --> Lakeview --> Tunnel --> Trailhead
This loop is probably just under 30 miles. I would choose this over Option #1 as you will see fewer people and you will get to hike through Andrews Bald.
Whichever option you choose, I would recommend calling the ranger station to inquire about conditions beforehand. We've had a ton of flooding rains this fall and some of the footbridges have been washed away. You don't want to be fording thigh deep whitewater in January!
Winter is the best time to visit Clingmans. Since the 7 mile paved road leading to it is closed, gaining access requires a minimum 14 mile RT hike. You'll probably it to yourself.