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.
Re Neanderthals more than likely diabetic. This does not make sense, as their diet probably had relatively little carbohydrate in it, being mostly meat based. Thus diabetes would not likely get expressed.