Both the structure and dynamics of biomolecules are known to be essential for their biological function. In the dehydrated state, the function of biomolecules, such as proteins, is severely impeded, so hydration is required for bioactivity. The dynamics of the hydrated biomolecules and their hydration water are related - but how closely? The problem involves several layers of complexity. Even for water in the bulk state, the contribution from various dynamic components to the overall dynamics is not fully understood. In biological systems, the effects of confinement on the hydration water further complicate the picture. Even if the various components of the hydration water dynamics are properly understood, which of them are coupled to the protein dynamics, and how? The studies of protein dynamics over the wide temperature range, from physiological to low temperatures, provide some answers to these question. At low temperatures, both the protein and its hydration water behave as solids, with only vibrational degrees of freedom. As the temperature is increased, non-vibrational dynamic components start contributing to the measurable dynamics and eventually become dominant at physiological temperatures. Thus, the temperature dependence of the dynamics of protein and its hydration water may allow probing various dynamic components separately. In order to suppress the water freezing, the low-temperature studies of protein rely on either low-hydrated samples (essentially, hydrated protein powders), or cryo-protective solutions. Both approaches introduce the hydration environments not characteristic of the protein environments in living systems, which are typically aqueous protein solutions of various concentrations. In this paper, we discuss the coupling between the dynamic components of the protein and its hydration water by critical examining of the existing literature, and then propose that proteins can be studied in an aqueous solution that is remarkably similar in its dynamic properties to pure water, yet does not freeze down to about 200 K, even in the bulk form. The first experiment of this kind using quasielastic neutron scattering is discussed, and more experiments are proposed.