The impact of a supercooled water droplet is considerably affected by the rapid crystal growth when the duration of the recalescence stage is comparable to the typical time of impact. However, the recalescence stage is generally neglected in the existing numerical simulations using the enthalpy-porosity method. We propose a subregion function method to deal with the rapid crystal growth during the impact of supercooled water droplets. A restricted region named the dendrite cloud region is defined in the method, and the phase change is enabled only in this dendrite cloud region while the evolution of this region is determined by the initial nucleation sites and the dendritic growth velocity of the ice. The impacts of supercooled water droplets on a smooth ice surface are simulated using a three-phase volume-of-fluid method coupled with the subregion function method. The calculated residual ice layer thickness at the impact center is consistent with previous experimental results. This subregion function method can also be extended to the numerical simulations of other types of fluid flows involving rapid solidification.