Why?
Both poles are cold mainly because they get less sunlight than other latitudes. Both receive 6 months continuous darkness, and the sun only rises to a small angle from the horizon, and have to travel through more atmosphere (which reduces the intensity of the sun’s rays); additionally, due to the low angle and white ice most of the rays are reflected off the surface back into space.

The difference between the two is that the South pole is located on a thick sheet of ice (miles thick), which itself is on a land mass (higher elevation). In contrast, the North pole is located at sea level in the Arctic Ocean, and the body of water helps to mediate temperatures (the water basically acts as a heat reservoir).

You can find more information at:
Scientific American:
South_pole_colder