Aqueous solutions of poly(vinyl methyl ether) are experimentally studied at temperatures below the equilibrium freezing temperature of water. Earlier investigations of the peculiar phase behavior of PVME/water gave evidence of the existence of a molecular solvent/polymer complex in which (at most) two water molecules per repeating unit are hydrogen bonded to the polymer chain. In favor of the complex formation hypothesis is the abrupt arresting of the crystallization and melting of water in mixture with omega(PVME) > 0.61. To relate this peculiar crystallization behavior and complex formation to the thermal and kinetic stability of the complex, the crystallization of water is explored in detail using thermal, volumetric, spectroscopic, X-ray scattering techniques, and morphological investigations. Our results clearly indicate the significant influence of the experimental conditions on the crystallization and subsequent melting of water. In agreement with previous results and for certain experimental conditions used in this study, the existence of a molecular complex is confirmed. However, additional experiments demonstrate that the complex is thermodynamically unstable and is only observed under certain kinetic conditions. For polymer concentrations omega(PVME) < 0.61 (almost) full crystallization of water can be realized by isothermal annealing in the temperature region -20 to -30 degreesC or slow cooling to low temperature. Furthermore, also in the concentration range omega(PVME) > 0.61 the crystallization of water can be realized provided the nucleation of water is facilitated. It is anticipated that the crystallization under previously employed crystallization conditions does not occur because the activation energy for nucleation is too large under the experimental conditions, and it is the nucleation that is arrested.