Neither of our neighbors, Lakes or Madison, nor the summit itself, Washington, are stingy on their water this time of year. What you may have heard are the huts that are open in winter are stingy with their water. The huts themselves do not require pumping. In addition to the huts, there are some springs across the summits. Some of them are well marked, others are not. Most maps today have their locations marked though. And with the correct supplies, you can get water nearly anywhere. I would recommend 2 liters by use of either two nalgens or one nalgen and a camel bag. But this is dependant on how fast you drink water. But rather than carry extra weight, I would highly recommend packing iodine tablets or if you have a water pump just in case you find yourself needing more water. Never drink water that is untreated. I have done this twice in the whites from marked springs and gotten mildly sick.
Also, on a side note, on the northern slope of the summit cone of Mt Washington, the water you see flowing is not a spring. It is either run-off or water perkulating from our leech fields. Can't tell ya how many times we have to explain that to people during the summer.
Staff Meteorologist/Night Observer, KMWN (Mt Washington Obs., NH)