I guess something fairly simple - a hole in the ground. Or it gets bagged and put into waste drums (or deposited directly) - this is still what we do at outbuildings where there's no sewage or water infra.
The answer is probably on Bill Spindler's website somewhere (southpolestation.com).
At Summit Station in Greenland (much smaller than Pole, Pole feels like a luxury resort comparitively), an outfall hole + usually we use the outhouses (which are just made using hot air).
Fresh water comes from the snow cave, and shoveled into the water melter.