Globular proteins undergo structural transitions to denatured states when sufficient thermodynamic state or chemical perturbations are introduced to their native environment. Cold denaturation is a somewhat counterintuitive phenomenon whereby proteins lose their compact folded structure as a result of a temperature drop. The currently accepted explanation for cold denaturation is based on an associated favorable change in the contact free energy between water and nonpolar groups at colder temperatures which would weaken the hydrophobic interaction and is thought to eventually allow polymer entropy to disrupt protein tertiary structure. In this paper we explore how this environmental perturbation leads to changes in the protein hydration and local motions in apomyoglobin. We do this by analyzing changes in protein hydration and protein motion from molecular dynamics simulation trajectories initially at 310 K, followed by a temperature drop to 278 K. We observe an increase in the number of solvent contacts around the protein and, in particular, distinctly around nonpolar atoms. Further analysis shows that the fluctuations of some protein atoms increase with decreasing temperature. This is accompanied by an observed increase in the isothermal compressibility of the protein, indicating an increase in the protein interior interstitial space. Closer inspection reveals that atoms with increased compressibility and larger-than-expected fluctuations are localized within the protein core regions. These results provide insight into a description of the mechanism of cold denaturation. That is, the lower temperature leads to solvent-induced packing defects at the protein surface, and this more favorable water-protein interaction in turn destabilizes the overall protein structure.