Bimolecular collision rate constants of a model solute are measured in water at T = 259-303 K, a range encompassing both normal and supercooled water. A stable, spherical nitroxide spin probe, perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl, is studied using electron paramagnetic resonance spectroscopy (EPR), taking advantage of the fact that the rotational correlation time, tau(R), the mean time between successive spin exchanges within a cage, tau(RE), and the long-time-averaged spin exchange rate constants, K-ex, of the same solute molecule may be measured independently. Thus, long- and short-time translational diffusion behavior may be inferred from K-ex and tau(RE), respectively. In order to measure K-ex, the effects of dipole-dipole interactions (DD) on the EPR spectra must be separated, yielding as a bonus the DD broadening rate constants that are related to the dephasing rate constant due to DD, W-dd. We find that both K-ex and W-dd behave hydrodynamically; that is to say they vary monotonically with T/eta or eta/T, respectively, where eta is the shear viscosity, as predicted by the Stokes-Einstein equation. The same is true of the self-diffusion of water. In contrast, tau(RE) does not follow hydrodynamic behavior, varying rather as a linear function of the density reaching a maximum at 276 +/- 2 K near where water displays a maximum density.