This is what is says under laws and policies at the park's website:Saltysack's answer to my question is sufficient to identify it as a legal service animal and the park indicates no restriction on this according to their website. The thread is not about service animals, everyone please don't hijack it further on that topic.Dogs and other pets (except service animals) are prohibited on any park trail except the Gatlinburg Trail and the Oconoluftee River Trail. (Compendium of Regulations, Pets, Section 2.15 (a)(1),
Hopefully both Saltysack and the service dog are properly acclimated to winter hiking in general. I hiked the park in the fall so I don't have any specific input regarding winter conditions. Four days through the park might be a bit quick depending on your hiking speed though. I reduce my mileage the most in the winter due to heavier equipment, boots, weather, daylight, etc. There may be road closings too in the winter? Again not much I know about it but I seem to recall a spring trip where a was potentially still closed. Consider your bailout options carefully.
There's no parking at Davenport Gap but down the road, maybe 1-2 miles, is a trailhead or campground or ranger station I forget it's been a while where you can park. There's a side trail off the AT that leads there.