Multinuclear spin-lattice relaxation rates and self-diffusion coefficient measurements are reported over wide ranges of temperature, pressure, and concentration in undercooled aqueous solutions of tetramethylammonium bromide. These dissolved organic cations with apolar surface groups provide model systems to investigate the effect of Coulombic, hydrophobic, and H-bond interactions upon the solvent and solute dynamics within the random, transient H-bond network of the water. Also reported for the first time are neutron diffraction difference experiments in these undercooled solutions to investigate how changes in dynamic disorder are related to changes in the average static structure of the hydration water as temperature is decreased. A substantial sharpening of the orientational order between water molecules is observed in the undercooled state.