Photosynthetic eukaryotic algae survived the Neoproterozoic Snowball Earth events, indicating that liquid-water refugia existed somewhere on the surface. We examine the potential for refugia at the coldest time of a snowball event, before CO₂ had risen and with high-albedo ice on the frozen ocean, before it became darkened by dust deposition. We use the Community Earth System Model to simulate a “modern” Snowball Earth (i.e., with continents in their current configuration), in which the ocean surface has frozen to the equator as “sea glaciers”, hundreds of meters thick, flowing like ice shelves. Despite global mean surface temperatures below -60°C, some areas of the land surface reach above-freezing temperatures because they are darker than the ice-covered ocean. With low CO₂ (10 ppm) and land-surface albedo 0.4 (characteristic of bright sand-deserts), 0.1 percent of the land surface could host liquid water seasonally; this increases to 12 percent for darker land of albedo 0.2, characteristic of polar deserts. Narrow bays intruding from the ocean to these locations (such as the modern Red Sea) could provide a water source protected from sea-glacier invasion, where photosynthetic life could survive. The abundance of potential refugia increases more strongly in response to reducing the land albedo than to increasing the CO₂, for the same global radiative forcing.