In any case, I think you have the right idea. A liquid "boils" when its vapour pressure is equal to the ambient pressure, and bubbles of vapour form directly in the liquid. The "normal boiling point" is specified when the ambient pressure (and thus also the vapour pressure of the liquid) is "1 atmosphere" (of course now we're down here on Earth).
At 100 ""^@C, water has a vapour pressure of 1*atm. The temperature of the moon varies between -150 ""^@C, and over 100 ""^@C. However, the ambient pressure is much, much lower than on Earth. Even on the dark side of the moon, water is likely to exist as vapour (even ice has a vapour pressure). This site estimates that the pressure on the moon is 3xx10^-15 atm. Lunar water is thus likely to exist in the gaseous phase.
