The thermal and moisture regimes of arctic and subarctic soils act in parallel in a complex manner and must be considered together. The problem of moisture movement and storage in these soils is complicated by water undergoing a phase change during freezing and thawing and by the presence of ice-rich permafrost. A one-dimensional model of these processes is developed and is based on an equivalent quasilinear variational functional for the Richards equation and the heat conduction equation including convective components. The variational functional is solved by a finite element analog. Convergence and stability are investigated, and it is concluded that the numerical procedure is convergent and stable in general.