Todd Rae and colleagues argue that the Neanderthal face was not adapted for extreme cold in this article in the Journal of Human Evolution.
The paper tackles two major assumptions about the paranasal sinuses: (1) big paranasal sinuses are good for surviving really cold weather and (2) that Neanderthals had really big paranasal sinuses.
The authors conducted a study of 2D and 3D X-rays on a sample of humans, other primates, and rodents. They showed that arctic critters actually exhibit smaller paranasal sinuses, not larger ones. Furthermore, when you correct for the size of the cranium, the sinuses of Neanderthals weren't any bigger than those of humans living in temperate latitudes.