We report shear viscosity of heavy water supercooled $33\,\mathrm{K}$ below its melting point, revealing a 15-fold increase compared to room temperature. We also confirm our previous data for the viscosity of supercooled light water, and reach a better accuracy. Our measurements, based on the spontaneous Brownian motion of $350\,\mathrm{nm}$ spheres, disagree at the lowest temperature with the only other available data, based on Poiseuille flow in a narrow capillary, which may have been biased by electro-osmotic effects. The viscosity ratio between the two isotopes reaches 2.2 at the lowest temperature. A companion Letter [F. Caupin, P. Ragueneau, and B. Issenmann, arXiv:2112.09010] discusses this giant dynamic isotopic effect. Here we provide a detailed description of the experiment and its analysis. We review the literature data about dynamic properties of water (viscosity, self-diffusion coefficient, and rotational correlation time), discuss their temperature dependence and compare their decoupling in the two isotopes.