I'm not sure what Tesla uses, but it's definitely not some sort of OLED, because the black levels aren't anywhere near. Apparently one of the many rolling changes to the Model S has been improved contrast of the driver's display, so Tesla is definitely trying to ride the curve as these things improve.

My own Tesla (a late 2013 model) is perfectly fine in this regard, but then I think it's spent exactly one evening in its life in anything resembling below-freezing weather. Otherwise, well, it's Texas.

The real cold-weather issue isn't the LCDs as much as it's the battery pack. When the pack is cold, it has reduced regeneration capacity. Tesla indicates this with a line in the power meter. After you've driven a few miles, the pack warms up and the problem goes away. If, however, you live at the top of a hill, parking outdoors in a cold climate, and your initial commute is downhill, then this lack of regeneration capacity would be an issue.