Degradation of near-surface permafrost due to changes in the climate is expected to impact the hydrological, ecological and biogeochemical responses of the Arctic tundra. From a hydrological perspective, it is important to understand the movement of the various phases of water (gas, liquid and ice) during the freezing and thawing of near-surface soils. We present a new non-isothermal, single-component (water), three-phase formulation that treats air as an inactive component. This single component model works well and produces similar results to a more complete and computationally demanding two-component (air, water) formulation, and is able to reproduce results of previously published laboratory experiments. A proof-of-concept implementation in the massively parallel subsurface flow and reactive transport code PFLOTRAN is summarized, and parallel performance of that implementation is demonstrated. When water vapor diffusion is considered, a large effect on soil moisture dynamics is seen, which is due to dependence of thermal conductivity on ice content. A large three-dimensional simulation (with around 6 million degrees of freedom) of seasonal freezing and thawing is also presented.