The Earth's climate has alternated between glacial and interglacial stages, but we still do not understand how the changes in insolation have been amplified by the climate system to lead to such a large climatic response. Here we use a climate model of intermediate complexity to show that the orbitally induced shift from an interglacial to a pre-glacial climate is highly sensitive to the high northern latitudes moisture budget. Using the insolation forcing alone, the model produces a first order response of sea surface temperatures and thermohaline circulation evolution which agrees with the available geological data. Under the same gradual insolation evolution, adding a small freshwater input into the Arctic Ocean induces a rapid climate switch from an interglacial to a pre-glacial mode. These results suggest a simple connection between orbital forcing and the thermohaline circulation through a freshwater threshold within the ocean-atmosphere-sea-ice system.