Great Smoky Mountains National Park
With fires, the forest cover and climate generally control what are the worse seasons for fires, add to this the human factor, accidental and prescribed burning.  For purposely ignited fires spring and fall are the major seasons, spring because the ground is often still damp but the fine fuels on the surface are dry enough to burn, making the fire easier to control, fall because the fuel is generally dry but the weather is getting colder and wetter with winter approaching making the fire easier to extinguish and reducing the time required to monitor the fire.  

In the case of the Smoky mountains, it appears that the weather is more damp, humid, in the winter and summer, additionally, summer has more moderating green moist vegetation that is not present in the spring or fall.  The following excerpt from the Great Smokey Mountains Fire management plan directly mentions the spring and fall seasons (See page 16).  Great Smoke Mountains Fire Management Plan  


  The annual fire weather cycle is more a function of seasonality and temperature than
  precipitation. Warm temperatures and exposed fuels during the dormant seasons of spring and
  fall condition the fuels for easy ignition and spread. In contrast, during the winter, cold
  temperatures prolong the wetting effect of the precipitation, and in the summer, heavy sheltering
  of fuels by tree foliage (coupled with high humidity) makes for poor ignition conditions under
  normal circumstances. Exceptions to the norm have occurred. Atypical dry spells in any
  season can result in more fires and/or unusually higher fire intensities. In 1987, and again in
  2007, extreme summer-time droughts made the normally fire-resistant hardwood forest
  susceptible to fire. Numerous lightning- and human-caused fires in and near the Park burned
  thousands of acres during summer months in those years.