The conformational flexibility of a protein and its ability to form hydrogen bonds with water are expected to influence the microscopic properties of water layer hydrating the protein. Detailed molecular dynamics simulations with an aqueous solution of the globular protein barstar have been carried out to explore such influence on the low-frequency vibrational spectrum of the hydration water molecules. The calculations reveal that enhanced degree of confinement at the protein surface on freezing its local motions leads to increasingly restricted oscillatory motions of the hydration water molecules as evident from larger blue shifts of the corresponding band. Interestingly, conformational fluctuations of,the protein and electrostatic component of its interaction with the solvent have been found to affect the transverse and longitudinal oscillations of hydration water molecules in a nonuniform manner. It is further noticed that the distributions of the low-frequency modes for the water molecules hydrogen bonded to the residues of different segments of the protein are heterogeneously altered. The effect is more around the frozen protein matrix and agrees well with slower protein-water hydrogen bond relaxations.