One of the limits of planetary habitability of Earth and other water-rich planets relates to the instability with respect to global glaciation, a fundamental property of the climate system caused by the positive ice-albedo feedback. Due to the steady increase in solar luminosity, the atmospheric concentration of carbon dioxide (CO2) at which this Snowball bifurcation occurs evolves over time. Earlier studies on the limit of global glaciation are based on investigations with very simple climate models for Earth’s entire history or studies of individual time slices carried out with a variety of more complex models and for different boundary conditions, making comparisons difficult. Here we use a relatively fast coupled climate model of intermediate complexity to trace the Snowball bifurcation of an aquaplanet through Earth’s history in one consistent modelling framework. We find that the critical CO2 concentration decreases more or less logarithmically with increasing solar luminosity until about 1 billion years ago, but drops faster in more recent times. Furthermore, there is a fundamental shift in the dynamics of the critical state about 1.8 billion years ago, driven by the interplay of wind-driven sea-ice dynamics and the surface energy balance. These results highlight once again the importance of climate dynamics for investigations of planetary habitability.