Using a combination of dielectric spectroscopy and solid-state deuteron NMR, the hydration water dynamics of connective tissue proteins is studied at sub-ambient temperatures. In this range, the water dynamics follows an Arrhenius law. A scaling analysis of dielectric losses, 'two-phase' NMR spectra, and spin-lattice relaxation times consistently yield evidence for a Gaussian distribution of energy barriers. With the dielectric data as input, random-walk simulations of a large-angle, water reorientation provide an approximate description of stimulated-echo data on hydrated elastin. This secondary process is quasi-isotropic and delocalized. The delocalization is inferred from previous NMR diffusometry experiments. It is emphasized that the phenomenology of this process is shared by many non-aqueous binary glasses in which the constituent components exhibit a sufficient dynamical contrast.