Can commercial airliners fly over central Antarctica during winter?
Surface air temperatures aren't really going to be relevant for an airliner. The temperature of the troposphere doesn't vary that much. In fact, the troposphere is warmer at the poles (from Wikipedia Troposphere):


  At middle latitudes, tropospheric temperatures decrease from an average of 15 °C at sea level to about −55 °C at the tropopause. At the poles, tropospheric temperature only decreases from an average of 0 °C at sea level to about −45 °C at the tropopause. At the equator, tropospheric temperatures decrease from an average of 20 °C at sea level to about −70 to −75 °C at the tropopause.


Sightseeing flights are indeed run during the summer months, but that is because it's actually possible to see things, not because it's any warmer. It wouldn't be very interesting to do a sightseeing flight in darkness.

The biggest obstacle to doing winter commercial flights over Antarctica is the lack of suitable alternate places to land in the event of an emergency.