This paper presents a sea ice prognostic model involving a one‐dimensional thermodynamic diffusion model, nudging satellite‐derived snow/ice temperatures, and two‐dimensional Lagrangian ice tracking. The aim of the model is to produce the evolvement of the physical properties of the snow and ice over the Arctic Ocean during the winter season. While the one‐dimensional column process solves the solution at a specific time and location, the evolvement of physical properties of the same ice target can be continuously simulated along the trajectory of ice movement determined by the Lagrangian tracking method. The main inputs were reanalysis‐based atmospheric forcings, thermal conditions constrained through nudging of snow skin temperature and snow‐ice interface temperature, and satellite‐derived ice motion vectors. The simulation results showed that the model can successfully reproduce well‐known regional features and geographical distributions of snow depth and ice thickness. The model‐simulated variables (i.e., snow depth, total freeboard, ice freeboard, ice thickness, and temperature) showed high correlations with the in situ or satellite measurements. In particular, the simulated temperatures were in excellent agreement with drifting buoy measurements. Since the nudging of the satellite‐derived temperature data into the model improved the thermal structure considerably, these data appear to be a key element for the successful simulation of other variables as well.