In high-latitude oceans with seasonal ice cover, the ice and the low-salinity mixed layer form an interacting barrier for the heat flux from the ocean to the atmosphere. The presence of a less dense surface layer allows ice to form, and the ice cover reduces the heat loss to the atmosphere. The ice formation weakens the stability at the base of the mixed layer, leading to stronger entrainment and larger heat flux from below. This heat transport retards, and perhaps stops, the growth of the ice cover. As much heat is then entrained from below as is lost to the atmosphere. This heat loss further reduces the stability, and unless a net ice melt occurs, the mixed layer convects. Two possibilities exist: (1) A net ice melt, sufficient to retain the stability, will always occur and convection will not take place until all ice is removed. The deep convection will then be thermal, deepening the mixed layer. (2) The ice remains until the stability at the base of the mixed layer disappears. The mixed layer then convects, through haline convection, into the deep ocean. Warm water rises towards the surface and the ice starts to melt, and a new mixed layer is reformed. The present work discusses the interactions between ice cover and entrainment during winter, when heat loss to the atmosphere is present. One crucial hypothesis is introduced: "When ice is present and the ocean loses sensible heat to the atmosphere and to ice melt, the buoyancy input at the sea surface due to ice melt is at a minimum". Using a one-dimensional energy-balance model, applied to the artificial situation, where ice melts directly on warmer water, it is found that this corresponds to a constant fraction of the heat loss going to ice melt. It is postulated that this partitioning holds for the ice cover and the mixed layer in the high-latitude ocean. When a constant fraction of heat goes to ice melt, at least one deep convection event occurs, before the ice cover can be removed by heat entrained from below. After one or several convection events the ice normally disappears and a deep-reaching thermal convection is established. Conditions appropriate for the Weddell Sea and the Greenland Sea are examined and compared with field observations. With realistic initial conditions no convection occurs in the warm regime of the Weddell Sea. A balance between entrained heat and atmospheric heat loss is established and the ice cover remains throughout the winter. At Maud Rise convection may occur, but late in winter and normally no polynya can form before the summer ice melt. In the central Greenland Sea the mixed layer generally convects early in winter and the ice is removed by melting from below as early as February or March. This is in agreement with existing observations.