It's also very, very white
Well.... they did live in a glacial climate, for a lot longer than Caucasoids did. And some Neanderthal bones bore suggestions of rickets, suggesting that vitamin D was in short supply -- which would definitely cause selection for lighter skin colors.
It could be argued that blond/red hair, blue eyes, and fair skin tones got into the modern population via a very small amount of gene flow from Neanderthals -- who had a much longer time to accumulate the necessary mutations. The red hair gene is estimated to be 100,000 years old, and there are a few recorded cases (Spain and Israel) of Neanderthal-modern hybrid skeletons, so such a transfer could have happened. Once these genes entered the modern population, the glacial climate could have rapidly selectively amplified them, "whitening" the incoming moderns very rapidly.
Of course neither mitochondria nor y-chromosome haplotypes show any evidence of Neanderthal mixture, but, if the admixture was at a very low percentage to begin with, the scarce Neanderthal haplotypes could easily have been wiped out during the population bottlenecks of the last glacial maximum.
I believe the human population absord the neanderthal population by killing males and mating with females. Seems to have been a very popular thing to do back in the old prehistory days.
Blue/gray/green eyes are found (natively) ONLY in those regions formerly inhabited by Neanderthals: Europe and Middle East. Light eye color may be a Neanderthal legacy. (Please, no flames: I myself have blue eyes.)
Afrocentrists love this theory because if whites are part Neanderthall, it somehow makes us less human. So they'll want Neanderthals to be white (probably correctly) and King Tut to be a Subsaharan African (contrary to all known science.)
Of course the Afrocentrists have their own internal contradiction to deal with, namely 2 of their favorite dogmas, when combined, indict them:
(1) "Western Civilization is the root of all Evil", and
(2) "Blacks invented Western Civilization"
Oops!
Wouldn't it also be possible that the 'ginger gene' was a rare occurrence among H. sapiens sapiens which then got somewhat amplified during a cold spell such as the Younger Dryas?