Glycerol acts as a natural cryoprotectant by depressing the temperature of ice nucleation and slowing down the dynamics of water mixtures. In this work, we characterise dynamics – diffusion, viscosity and hydrogen bond dynamics – as well as density anomaly and structure of water mixtures with 1%–50% (w/w) glycerol at low temperatures via molecular dynamics simulations using all-atom and coarse-grained models. Simulations reveal distinct violations of the Stokes–Einstein relation in the low-temperature regime for water and glycerol. Deviations are positive for water at all concentrations, and positive for glycerol in very dilute solutions but turning negative in concentrated ones. The all-atom and coarse-grained models reveal an unexpected crossover in the dynamics of the 1% and 10 % (w/w) glycerol at the lowest simulated temperatures. This crossover manifests in the diffusion coefficients of water and glycerol, as well as in the viscosity and lifetime of hydrogen bonds in water. We interpret that the crossover originates on the opposing dependence with glycerol concentration of the two factors controlling the solutions' slow down: the increase in tetrahedrally coordinated water and the dynamics and clustering of the glycerol molecules. We anticipate that this dynamic crossover will also occur for solution of water with other polyols.