Cold adaptation by itself does not necessarily imply more intelligence. Neanderthal had a brain about 100 cc larger than modern humans, but that is not a huge difference. There is no evidence that 100 cc equates to smarter. The range of variation in modern humans is huge, and there is no evidence of which I am aware that 100 cc difference means anything in terms of intelligence.
Please google Neanderthals and burials you might learn something. While your ancestors left their dead relatives where ever they fell, Neanderthal tied his dead loved ones up in in a crouched position (the same position in which babies enter the world). Death for a Neanderthal was the return to the womb. This is very complicated thinking which some people even now days are incapable of grasping.I for one am very interested in knowing what the extra gray matter was capable of doing. I do not buy the B.S. that the extra gray matter of the Neanderthal was superfluous.
The complex behavior of Neanderthal appears to be confirmed by the evidence. What is not understood is why Neanderthal became extinct while modern humans thrived. It does appear that the extra 100 cc of gray matter was not a factor in this part of selection pressure. What was? Don't know.
If it gets your goat to learn that man is not the top of the pyramid as far as brains ,maybe some humility is just what you need.
The extra 100 cc of gray matter appears not to have made the critical difference: Neanderthal is extinct and H. sapiens are here today. Perhaps some other trait was more important?
When you figure absolute brain size you have to take into consideration body size. The primate line is clearly ahead of the pack in relative brain size (although whales and elephants are larger in absolute terms, they have much larger bodies to maintain). Within the primate line, how much larger would Neanderthal have had to be to have a 100 cc brain size increase? Perhaps 6 percent?
One method of adapting to cold climate is to develop a short, squat body form--an endomorph. That preserves heat because of the better volume to surface ratio. Perhaps Neanderthal did that; the osteology does not contradict this possibility. A change in only 6 percent of body mass could have lead to a similar change in brain size.
In either case, we still do not really know why Neanderthal went kaput and we survived. There is a lot more that science can tell us if we are patient. Maybe the DNA will provide some additional clues.