Recent experiments by Kavousanakis et al., Langmuir, 2018 [1], showed that reversible electrowetting on superhydrophobic surfaces can be achieved by using a thick solid dielectric layer (e.g. tens of micrometers). It has also been shown, through equilibrium (static) computations, that when the dielectric layer is thick enough the electrostatic pressure is smoothly distributed along the droplet surface, thus the irreversible Cassie to Wenzel wetting transitions can be prevented. In the present work we perform more realistic, dynamic simulations of the electrostatically-induced spreading on superhydrophobic surfaces. To this end, we employ an efficient numerical scheme which enables us to fully take into account the topography of the solid substrate. We investigate in detail the role of the various characteristics of the substrate (i.e. the dielectric thickness, geometry and material wettability) and present relevant flow maps for the resulting wetting states. Through our dynamic simulations, we identify the conditions under which it is possible to achieve reversible electrowetting. We have found that not only the collapse (Cassie-Baxter to Wenzel) transitions but also the contact angle hysteresis of the substrate significantly affects the reversibility.