A simple analytical model of the atmospheric boundary layer (ABL) coupled to sea ice is presented. It describes clear-sky cooling over sea ice during polar night in the presence of leads. The model solutions show that the sea ice concentration and wind speed have a strong impact on the thermal regime over sea ice. Leads cause both a warming of the ABL and an increase of stability over sea ice. The model describes a sharp ABL transition from a weakly stable coupled state to a strongly stable decoupled state when wind speed is decreasing. The threshold value of the transition wind speed is a function of sea ice concentration. The decoupled state is characterized by a large air-surface temperature difference over sea ice, which is further increased by leads. In the coupled regime, air and surface temperatures increase almost linearly with wind speed due to warming by leads and also slower cooling of the ABL. The cooling time scale shows a nonmonotonic dependency on wind speed, being lowest for the threshold value of wind speed and increasing for weak and strong winds. Theoretical solutions agree well with results of a more realistic single-column model and with observations performed at the three Russian "North Pole" drifting stations (NP-35, -37, and -39) and at the Surface Heat Budget of the Arctic Ocean ice camp. Both modeling results and observations show a strong implicit dependency of the net longwave radiative flux at the surface on wind speed.