The horizontal resolution in numerical weather prediction models can have a large impact on the quality of polar low forecasts. However, there are few studies on the effect of the horizontal grid spacings which are currently in operational use at the European Centre for Medium-Range Weather Forecasts (ECMWF). Here, we evaluate the 10 m wind speed forecasts for four polar lows in November and December 2016 against remote and in situ observations. We study the 18 km grid spacing, used in the ensemble, 9 km for the current operational deterministic model runs, and 5 km for the planned future deterministic runs. The 9 and 5 km versions fall within the range of grid spacings that resolve convection partly but not fully. Therefore, we also do sensitivity tests with and without deep convection parametrization. Finally, we examine the added value from the operational limited-area model AROME-Arctic with 2.5 km grid spacing. The 18 km version performed worst in magnitude of wind speed, but it did forecast the locations of the polar lows as well as the other models. Thus, the ensemble can be used for polar low probability products. The 5 and 9 km versions with parametrized convection were the best-performing models over the ocean, while AROME-Arctic was the best model along the coast and over land. The 5 and 9 km versions with resolved deep convection produced fewer but larger convective cells with patches of both under-and overestimation of wind speed. The fact that there was almost no difference between the 9 and 5 km grid spacing, but a clear impact from the handling of convection, suggests that, to improve polar low forecasts in the ECMWF deterministic runs, special attention to convection is needed.