A quasiclassical trajectory calculation is performed for the Penning ionization system H2O+He*(2(3)S)-->H2O+(B-2(2),(2)A(1),B-2(2)) + He + e(-) at H2O rotational temperatures of 300, 200, 100, and 25 K. The resonance potential and the widths for the three ionized states are fitted to analytical functions on the previous ab initio points [J. Chem. Phys. 102, 4169 (1995)]. The calculational results are compared with experimental measurements. The total and partial ionization cross sections are calculated in the energy range 0.05-1.0 eV. As the rotational temperature is lowered, the following results are predicted : the total cross section decreases with collision energy, and the dominant ionization into the (2)A(1) state is more enhanced. These results are due to the increasing drawing of trajectories into the attractive H2O lone pair region with decreasing rotation frequency. Opacity functions and total and partial ionization probabilities for each trajectory are analyzed to interpret the results obtained for the cross sections.