Neanderthals had short stocky bodies perfectly suited to the cold.  Modern humans had tall skinny bodies, terribly suited to the cold. Yet despite being at a physical disadvantage, modern humans had the intelligence to adapt the situation to their advantage.  The BBC writes:

…Neanderthals, with their shorter and stockier bodies, were actually better adapted to Europe’s colder weather than modern humans. They came to Europe long before we did, while modern humans spent most of their history in tropical African temperatures.  Paradoxically, the fact that Neanderthals were better adapted to the cold may also have contributed to their downfall.

If that sounds like a contradiction, to some extent it is.

Modern humans have leaner bodies, which were much more vulnerable to the cold. As a result, our ancestors were forced to make additional technological advances. “We developed better clothing to compensate, which ultimately gave us the edge when the climate got extremely cold [about] 30,000 years ago,”…

If this analysis is correct, it provides strong support for the cold winters theory of human population differences in IQ, because it suggests cold climates were so cognitively demanding for hominins, that not even Neanderthals, whose bodies were physically adapted to the cold, could survive when it got really cold.