According to Physics Today, the lowest naturally occurring temperature on our planet, -150 o C, is not found in the depths of winter in Antarctica but high in Earth's atmosphere at an altitude of 80-85 km. There, as the mesosphere gives way to the thermosphere above it, the ambient temperature stops falling, reaches its global minimum, and begins climbing again.
A recent (June 2018) satellite study of temperatures in depressions in the Antarctic ice cap found a low of -144 Fahrenheit, and concluded that if very low velocity winds lasted for a week or so (so that the cold air was trapped in the depressions), the temperature in such depressions might get as low as -148 F. Even that would require the air above the depressions to be to be exceptionally dry (and clear), as even small amounts of water in the atmosphere would block surface radiation (and radiative cooling) at such low temperatures.