Everyone in the water tribes are reminescent of the Inuit peoples of Alaska, and being from the 49th state, I can say that the skin color of the Northern Water Tribe is quite accurate of the indigenous people of that region today.

I heard they either switched animators, or they switched the people who colored the animations. (You'll notice that there are several shots showing red-headed Water Tribe people too).

Whatever they did, there was a change in staff, and therefore the colors changed. It didn't really have anything to do with their actual race.

But if you were looking for a scientific response, ice and snow (which there is a lot of in the colder regions of the world), reflect the sun, and can actually cause sunburn. It's possible that once Katara was removed from the influence of snow glare, her skin lost some of it's tan and returned to it's un-sun influenced shade.