Motivated by recent experiments showing the promise of noble gases as cryoprotectants, we perform molecular dynamics modeling of phase transitions in water with xenon under cooling. We follow the structure and dynamics of xenon water solution as a function of temperature. Homogeneous nucleation of clathrate hydrate phase is observed and characterized. As the temperature is further reduced we observe hints of dissociation of clathrate due to stronger hydrophobic hydration, pointing towards a possible instability of clathrate at cryogenic temperatures and conversion to an amorphous phase comprised of "xenon + hydration shell" Xe·(H2O)21.5 clusters. Simulations of ice-xenon solution interface in equilibrium and during ice growth reveal the effects of xenon on the ice-liquid interface, where adsorbed xenon causes roughening of ice surface but does not preferentially form clathrate. These results provide evidence against the ice-blocker mechanism of xenon cryoprotection.