A quantitative picture of the effect of low-temperature exposure on the survival of living cells is presented through discussion of solutions to a differential equation relating the volume of intracellular water to the temperature, the cooling rate, and various cell parameters. It is found that for a given cell, a single parameter which depends on the cooling rate governs the behavior of the cell when it is exposed to low temperatures. The analysis develops relationships between solutions to the differential equation and the phenomena affecting cell survival, namely, intracellular freezing and cell dehydration. Theoretical predictions are found to agree well with existing experimental observations.