phat, guys,
I need water in the night. It doesn't do me any good buried in the snow. I might need to take some Tylenol or Diamox or something or just be thirsty, or need to chase some chocolate doughnut. As far as water to start the morning melt, some already melted water helps but isn't required.
Note for new winter campers. You cannot melt snow directly on a hot stove, it will scorch the pan and taste horrible and be full of metal ions, thus as phat points out, 3-4 ounces of water to start with is a good idea, then do not add enough snow at any one time to absorb all of the water and again scorch the pan. It will steam and burn without actually melting.

To melt snow without any liquid water to start do this. Light your stove and keep it low. Hold the pan above the stove to WARM it and add one teaspoon of snow - no more, and swish it around until it melts, then add one more teaspoon, don't hurry it, and hold the pan maybe 6 inches above your stove. When the second teaspoon is melted, add a third, in about 2 minutes you will have 3-4 ounces of water and an unscorched pan, then you can add an amount of snow approximately equal to the teaspoons that you used, but never enough to absorb all of the water. If you heat the water in the pan so that its hot before adding more snow it will help eliminate the absorption problem. I personally use the heat it up then add more method, others simply add slowly and continuously, whatever method you use, do stir constantly.
Jim