Modeling air-sea interactions during cold air outbreaks poses a major challenge because of the vast range of scales and physical processes involved. Using the Polar WRF model, we investigate the sensitivity of downstream air mass properties to (a) model resolution, (b) the sharpness of the marginal-ice zone (MIZ), and (c) the geometry of the sea ice edge. The resolved sharpness of the MIZ strongly affects peak heat fluxes and the atmospheric water cycle. For sharper MIZs, roll convection sets in closer to the sea ice edge, increasing both evaporation and precipitation. This yields an increased heat transfer into the atmosphere while the net effect on the atmospheric moisture budget is small. Consequently, higher atmospheric resolution increases the probability that a cold-air outbreak triggers deep convection in the ocean. The geometry of the sea ice edge can induce convergence or divergence zones that affect the air-sea exchange.