Marine ice cover in the frigid Neoproterozoic climate system tends to isolate the ocean: the thickness of this ice, and thus the degree of isolation, is an important unknown in geochemical and biological arguments regarding the fully-glaciated "Snowball Earth" hypothesis. The Pollard and Kasting (2005) coupled atmosphere/ice model has been modified to track ice of marine and atmospheric origin separately, and model their different optical properties. In contrast to Pollard and Kasting's results, a tropical region of thin ice is not stable in this model: ice is hundreds of meters thick everywhere. The overall pattern of the hydrological cycle in a Snowball climate is also discussed.