Water droplets released from the sea surface represent one of the major causes of ice accretion on marine vessels. A one-dimensional model of the freezing of a spherical water droplet moving in cold air was developed. The crystallization model allows one to obtain an analytical solution if a uniform temperature distribution over the liquid’s core is assumed. The model was validated using STAR CCM+ Computational fluid dynamics (CFD) code. A collision of a partially frozen droplet with a solid wall assuming the plastic deformation of an ice crust was also considered. The ratio of the crust deformation to the crust thickness was evaluated. It was assumed that if this ratio were to exceed unity, the droplet would stick to the wall’s surface due to ice bridge formation caused by the water released from the droplet’s core.