We investigate the water deuteration ratio and ortho-to-para nuclear spin ratio of H2 (OPR(H2)) during the formation and early evolution of a molecular cloud, following the scenario that accretion flows sweep and accumulate HI gas to form molecular clouds. We follow the physical evolution of post-shock materials using a one-dimensional shock model, with post-processing gas-ice chemistry simulations. This approach allows us to study the evolution of the OPR(H2) and water deuteration ratio without an arbitrary assumption concerning the initial molecular abundances, including the initial OPR(H2). When the conversion of hydrogen into H2 is almost complete, the OPR(H2) is already much smaller than the statistical value of three due to the spin conversion in the gas phase. As the gas accumulates, the OPR(H2) decreases in a non-equilibrium manner. We find that water ice can be deuterium-poor at the end of its main formation stage in the cloud, compared to water vapor observed in the vicinity of low-mass protostars where water ice is likely sublimated. If this is the case, the enrichment of deuterium in water should mostly occur at somewhat later evolutionary stages of star formation, i.e., cold prestellar/protostellar cores. The main mechanism to suppress water ice deuteration in the cloud is the cycle of photodissociation and reformation of water ice, which efficiently removes deuterium from water ice chemistry. The removal efficiency depends on the main formation pathway of water ice. The OPR(H2) plays a minor role in water ice deuteration at the main formation stage of water ice.
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