Recent results from the study of the interaction of Earth's moon with the solar wind have highlighted lunar surface charging as an important physical process not only for the local interaction of the surface and the impinging plasma but also for charged dust ejection and transport. Excluding Earth's moon, however, such studies have been limited to very few solar system bodies. Here we assess the importance of surface charging for the Saturnian plasma-absorbing moons. In this initial study, we focus on the various moons' trailing hemispheres and their variable charging patterns as a function of their magnetospheric local time. With only a few exceptions, our results indicate negative potentials for all moons, with the most extreme values predicted for Rhea. When the leading hemisphere is partially sunlit, the surface potential profile can be quite complex with many different transition regions. We also find that electrostatic acceleration of dust is at least equally as (if not more) important as it is for Earth's moon for the submicron grains, but it is probably not sufficient to explain the detection of the larger micron-sized grains in the vicinity of the large moons of the outer planets. Regarding Saturn's asteroid-sized moons, we predict that electrostatic forces can accelerate grains above the escape velocity and populate the Saturnian system and/or contribute to dust transport across those moons' surfaces. On the basis of these results, we also propose several methods by which Cassini's instruments could be used to directly observe the effects of surface charging.