Simulations of frigid Neoproterozoic climates have not considered the tendency of thick layers of floating marine ice to deform and spread laterally. We have constructed a simple model of the production and flow of marine ice on a planetary scale, and determined ice thickness and flow in two situations: when the ocean is globally ice-covered (hard snowball) and when the tropical waters remain open (soft snowball). In both cases, ice flow strongly affects the distribution of marine ice. Flowing ice probably carries enough latent heat and freshwater to significantly affect the transition into a Snowball Earth climate. We speculate that flowing marine ice, rather than continental ice sheets, may be the erosive agent that created some Neoproterozoic glacial deposits.