While Neanderthal probably did not consume milk other than from their mothers, they probably crunched a lot of bones and marrow. Also, their pale skin, redhead, blue eyed traits made it especially easy for them to utilize what little sun their were exposed to to form Vitamin D in their skin and absorb it for bone building. When our European ancestors, had a white skin gene mutation, it accelerated their ability to move north, but some also probably bred with Neanderthals and got the redhead, pale skin gene which also facillitated their move north. Thus there are probably two distinct classes of “white” people. Would be interesting to see genetic research on that. I think my late husband probably had some of those Neanderthal genes. Scotish ancestry, acute sun sensitivity.
The Neanderthals had one ~ the red/yellow allele, and white folks got two ~ the red/yellow and the brown/black allele.
The blue-eyed trick is not unique to humans. Arctic dogs have blue eyes, and barring horizontal gene transfer, they must have come by the series of mutations that make that possible all on their own.
Now, for light skin ~ that takes a bunch of mutations, some of which are tied into the adult ability to consume milk. I haven't seen any information that says the Neanderthals have all of them, but they did have essentially the same major genes suppressing pigment as West Asians (white folks), but not the same genes that are used in East Asians to suppress pigmentation.
I will take a wild guess that the Neanderthals had one or more of the alleles that causes "intermittent Scandinavian porphyria". They were more than likely diabetic ~ 'cause all that extra sugar in your system serves as antifreeze.
The Europeans are the ones with virtually all the red-heads though!