Sorry, that is Lamarckism, and it is not how evolution works. Evolution reflects the natural world and may appear much crueler. One thing to remember is that there is always variation. Some people will have more melanin and some will have less, and there is a genetic reason for this A person with a low amount of melanin in a sun intense area is more likely to get skin cancer and die. If this happens before he breeds or if his offspring die due to his early death his early demise his DNA will drop from the genome. If this happens often enough There will be only dark skinned individuals left. The lighter skinned people would have been "selected" out.
I think that dark skinned people came from Africa (where they now reside), and some moved north to the colder climates. For some reason, their skin color got lighter, and their hair color and eye color also did (at least in some cases).
If it is true that creatures are white to avoid being seen in white snow, then smaller animals (prey) are white so they won't be eaten, and larger animals (predators) are white so they can sneak up on prey. In either case, blending in with snow would be naturally selected (Darwin's idea of natural selection) because they could survive better.
I think that too little time passed for humans to evolve light skin, light eyes, and light hair in colder climates. Do we see that happening among Eskimos, who have black hair? Rather, I specualte that the inbreeding that we know occurred between humans and Neanderthals might have passed light color genes to humans. However, studies of red haired Neanderthal prove that humans didn't inherit that gene from Neanderthals. But could Neanderthals have had another gene, that was the same as humans, that passed to humans?