I agree with the rest on not leaving a car at Elk Garden. I hike this area a lot and you have plenty of good options.
- If you are set on the trip you outlined then use the shuttle service.
- I typically park at Massie Gap and have done a lot of loops. I have never had any issues.
- I have also parked at Beartree Lake in the fisherman's parking lot without any issue. It's a quick hike to the AT or Iron Mtn trail. Makes for a excellent long loop. You can also do a point to point and choose from many shuttle pickup locations (whitetop, elk garden, massie gap, fox creek, etc).
Massie's Gap allows you to start at a higher altitude whereas Beartree is a low elevation start. If the snow is bad and the access roads are closed you can start your hike low where parking and roads are better.
Your hike looks to be around 17 miles, so you could easily put together a loop from Massie's Gap at that distance. The crowds are gone so you would have the area to yourself. Their are great campsites around the AT at Rhododendron gap, Bearpen Trail, Scales Trail, Stone Mountain on AT, etc.
You can also park at Massie's Gap after dark and do a night hike over Wilburn Ridge without any issue.
As the others have said check the weather often because it changes fast. I had a trip planned to this area last weekend. On Wed it looked like light snow and cold temps. By Thursday afternoon they were calling for 2 feet of snow and extreme cold. Be prepared to have a great time or maybe postpone your trip.
Probably more than you wanted.