I've heard of a few moons in the solar system that have water, like europa and enceladus. However, I can't find information about whether there are other moons as well. I'm guessing there are more, but I'm not totally sure.
How many moons in the solar system have water (either liquid or frozen)?
It's probably easier to consider the reverse question: which ones don't have water.
Talking about the major satellites of the planets, there are only two which are not ice moons: our own Moon, which has ice deposits at the poles, and Io. As far as I am aware, the evidence for water on Io is tentative at best (e.g. Douté et al. 2004), so of the major planetary satellites, the answer is all of them have water (usually in the form of ice, but some of them also have liquid subsurface oceans) with the possible exception of Io.
The small satellites of the giant planets are probably icy but I'm not sure the possibility that one or two of them are dry rocky asteroids that have been captured has been fully excluded. Phobos and Deimos have rocky surfaces but the possibility of ice in the interior of the Martian moons has not been ruled out.
There are probably lots of ice-free asteroid moons but finding out which ones they are would require going there and checking whether there's any ice in the subsurface, so confirming this is not currently possible. Small solar system bodies in the outer system are probably going to be icy, so dwarf planet satellites (Charon, Vanth, etc.) all likely contain ice.
