Avatar The Last Air Bender

Yea, cuz White people populate the Poles. If anything, Fire Nation should be white: India never tried to take over the world.

You seem to be forgetting the arctic circle includes a quarter of the Scandinavian Peninsula, and that lighter skin colorization is generally considered to be an adaptation to living in a low sunlight environment (the Inuit and Yupik you alluded to as being more likely polar candidates escaped that form of evolution due to their diet being high in vitamin D). The further a culture expanded from the equator the lighter they'd have become without other environmental factors.

Assuming, based on the Avatar world Map, the Earth Kingdom served the role of their Africa as the birthplace of humanity before the nomadic diaspora it would not be illogical for the natives of that country to be particularly dark, while the ones who moved into the poles became pale and the air islands became rather median. The fire nation being equatorial would likely remain as dark, or perhaps even go darker as the earth nation is large enough to have created a mellowing due to intermingling while the fire nation remained more tightly interbred and unvarying.