I think Cades Cove and Smokemount are the only two camp sites that are open the year around in the Natl Park. Neither camp ground has electric except maybe a couple of sites with 15AMP service for medical situation folks.
It can get pretty nasty there when it snows... Sure is a beautiful camp spot however with the adjoining CADES COVE motor/hiking trail... We really like the ELKMONT camp ground better but it is closed during the winter months.
It probably would be a good idea to checkin with the rangers before heading out - This area got hit pretty hard this year with flooding and lots of rain... Probably the best way in would be from the Townsend side during the winter months.
NOTE: I just noticed you have a 32-foot trailer... Although the roads in is ok for the big trailers you must be careful going around the many curves on the natl Park roads that have low overhang. Sometimes swinging wide to clear these curves gets exciting with on-coming traffic on the two lane roads. Just be watchful in these areas.
Roy Ken