Venchka is just responding to the earlier posters (OP included) and probably missed the AT part in the thread title.
On the AT, I don't recall encountering any restrictions on the type or seasonal restrictions. Were there any fire restrictions around the times of the Gatlinburg fire? An exception to that might be using wood burning stoves in areas where no fires are allowed, would be useful to know one way or the other. Barring any restrictions, I use whatever stove I feel like using based on the trip.