This work investigates the anti-ice performance of various superhydrophobic surfaces under different conditions. The adhesion strength of glaze ice (similar to that deposited during "freezing rain") is used as a measure of ice-releasing properties. The results show that the ice-repellent properties of the materials deteriorate during icing/deicing cycles, as surface asperities appear to be gradually damaged. It is also shown that the anti-icing efficiency of superhydrophobic surfaces is significantly lower in a humid atmosphere, as water condensation both on top of and between surface asperities takes place, leading to significantly larger values of ice adhesion strength. This work thus shows that superhydrophobic surfaces are not always ice-repellent and their use as anti-ice materials may therefore be limited.