Isn't that the truth about water everywhere?
But what an interesting question - what happens to greywater used in Antarctica? A quick search found some answers. At this site where anyone can ask a question about life "under down under", the resident reports: "Different camps produce different amounts of grey water. Obviously, it depends on how many people are in camp and how much water they use. Lake Hoare produces about 21 barrels of grey water each season. A barrel is a 55 gallon drum. Lake Hoare is a very active camp, with LOTS of people coming and going!". This is confirmed by this site on waste management, but there also appears to be some wastewater treatment available at a central location where barrels are hauled to and unloaded.
And another in a series of great greywater theses, this thesis completed at KTH Chemical Engineering and Technology in Sweden reports "A survey on waste water treatment on almost all Antarctic research stations has been carried out in order to find a suitable treatment method for the grey water released from Wasa. The survey showed that all twenty eight member states that operate research stations was included and the survey covered 41 permanent stations, 26 summer stations and 4 field stations. The study showed that 26 permanent stations and 8 summer stations had some kind of treatment for their waste water. The most common treatment method at the permanent stations are biological treatment (8 stations) followed by secondary treatment and maceration (4 stations per method)".
New Zealand researchers have built a wastewater treatment plant at their station in Antartica and apparently plan on treating greywater for flushing toilets in the future.
According to Dr. Isabella Velicogna of the Department of Earth System Science at the University of California Irvine "Antarctica is Earth's largest reservoir of fresh water". Given so much "water" why be concerned about reusing greywater in Antarctica?