This work is devoted to the development of a new hybrid VOF-IBM method for the simulation of freezing liquid films and freezing drops. The VOF and IBM methods are coupled with the temperature equation to be able to solve the icing front, the dilatation induced by the density difference between the liquid and the ice as well as the drop deformation induced by the balance of the surface tension and gravity. The numerical simulations are validated by a comparison between the theoretical solutions and experimental observations. We investigate the effect of the Stefan number and the ratio of solid density to liquid density on the height evolution of the icing front for both liquid films and drops. We also study the whole freezing processes of drops with different contact angles. Furthermore, the effect of gravity and the surface tension on freezing processes of drops are investigated. The temperature distribution, solidification shape, and evolution within the drop are systematically analyzed and the CSF-VOF spurious currents are shown to induce no effect on the icing process due to the small value of both the corresponding Weber and Capillary numbers. We find that the final drop shape is in very good agreement with experiments, and in particular the value of the tip angle of the iced drop and the front-to-interface angle are very well reproduced.