Poly(ethylene oxide) (PEO) is a well-known biocompatible polymer and has widely been used for medical applications. Recently, we have investigated the dynamic behavior of hydration water in the vicinity of PEO chains at physiological temperature and shown the presence of slow water with diffusion coefficient one order of magnitude less than that of bulk water. This could be evidence for the intermediate water that is critical for biocompatibility; however, its detailed dynamical features were not established. In this article, we analyze the quasi-elastic neutron scattering from hydration water through mode distribution analysis and present a microscopic picture of hydration water as well as its relation to cold crystallization.