The behavior of the terrestrial glacial regime during the Neoproterozoic glaciations is still a matter of debate. Some papers claim that the glacial sequences cannot be explained with the snowball Earth scenario. Indeed, the near shutdown of the hydrological cycle simulated by climatic models, once the Earth is entirely glaciated, has been put in contrast with the need for active, wet-based continental ice sheets to produce the observed thick glacial deposits. A climate ice-sheet model is applied to the older extreme Neoproterozoic glaciation (around 750 Ma) with a realistic paleogeographic reconstruction of Rodinia. Our climate model shows that a small quantity of precipitation remains once the ocean is completely ice-covered, thanks to sublimation processes over the sea-ice at low latitudes acting as a water vapor source. After 10 ka of the ice-sheet model, the ice volume in the tropics is small and confined as separate ice caps on coastal areas where water vapor condenses. However, after 180 ka, large ice sheets can extend over most of the supercontinent Rodinia. Several areas of basal melting appear while ice sheets reach their ice-volume equilibrium state, at 400 ka, they are located either under the two single-domed ice sheets covering the Antarctica and the Laurentia cratons, or near the ice-sheet margins where fast flow occurs. Only the isolated and high-latitude cratons stay cold-based. Finally, among the simulated ice sheets, most have a dynamic behavior, in good agreement with the needs inferred by the preserved thick formations of diamictite, and share the features of the Antarctica present-day ice sheet. Therefore, our conclusion is that a global glaciation would not have hindered the formation of the typical glacial structures seen everywhere in the rock record of Neoproterozoic times.