Walking on water

If you were on one of the tiny moons of Jupiter or Saturn and you dug down to the hypothesized liquid water, is the gravity low enough that you could walk on the water? If there were life in the water, would the creatures be super-heavy in order to swim around in the water under low gravity or would they walk upside-down on the underside of the icy surface because they are lighter than the water between the core and the ice? Would both forms exist? In this case, only the heavy can "fly".