The existence of photosynthetic eukaryotic algae during the so-called Snowball Earth events presents a conundrum. If thick ice covered the oceans, where could such life persist? Here we explore the possibility that photosynthetic life persisted at the end of long narrow seas, analogous to the modern-day Red Sea. In this first analytical model, we test the ability of the global sea glacier to penetrate a Red Sea analogue under climatic conditions appropriate during a Snowball Earth event. We find the Red Sea is long enough to provide a refugium only if certain ranges of climatic conditions are met. These ranges would likely expand if the restrictive effect of a narrow entrance strait is also considered.