Snowpack models assume that the ice and air phases of the snow matrix are in thermal equilibrium. This assumption is questionable for short time scales (15 min) and small layer heights (1 cm) required to model snow metamorphism and avalanche formation. In this paper, a nonequilibrium model is formulated, which contains: (1) two energy conservation equations for both the ice and air phases; (2) mass conservation equations for the interstitial air and water vapor; and (3) entropy production relations for the ice and air phases. The equations are closed by interfacial heat and mass transfer terms. Dimensionless numbers are stated and the criteria for equilibrium modelling are investigated. The governing equations are solved using an implicit finite element scheme, which includes temperature-dependent viscous deformations. The nonequilibrium model can accurately track measured temperature profiles in a seasonal snowpack using a multiphase, microstructure-based thermal conductivity law. Calculated temperature differences of several degrees between the ice and air below the top surface of the snowpack are found, revealing that interfacial heat transport between the ice and air has a significant impact on the thermal regime of the snowcover. A comparison between measurements and simulation results reveals bulk interfacial heat transfer coefficients h on the order 0.5 W m^-2 K^-1. Finally, we show that the alpine snowcover develops to a state of stationary entropy production during a winter season.