The dielectric relaxation process of water was investigated for polymer/water mixtures containing poly(vinyl methyl ether), poly(ethyleneimine), poly(vinyl alcohol), and poly(vinylpyrrolidone) with a polymer concentration of up to 40 wt % at frequencies between 10 MHz and 10 GHz in subzero temperatures down to -55 degrees C. These polymer/water mixtures have a crystallization temperature T-C of water at -10 to -2 degrees C. Below T-C, part of the water crystallized and another part of the water, uncrystallized water (UCW), remained in a liquid state with the polymer in an uncrystallized phase. The dielectric relaxation process of UCW was observed, and reliable dielectric relaxation parameters of UCW were obtained at temperatures of -26 to -2 degrees C. At T-C, the relaxation strength, relaxation time, and relaxation time distribution change abruptly, and their subsequent changes with decreasing temperature are larger than those above T-C. The relaxation strength of UCW decreases, and the relaxation time and dynamic heterogeneity (distribution of relaxation time) increase with decreasing temperature. These large temperature dependences below T-C can be explained by the increase in polymer concentration in the uncrystallized phase C-p,C-UCP with decreasing temperature. C-p,C-UCP is independent of the initial polymer concentration. In contrast to the relaxation times above T-C, which vary with the chemical structure of the polymer and its concentration, the relaxation times of UCW are independent of both of them. This indicates that the factor determining whether the water forms ice crystals or stays as UCW is the mobility of the water molecules.