A lattice Boltzmann method (LBM) two-dimensional (2D) mesoscopic model is presented for studying the frost crystal nucleation process involved in liquid-solid phase change on a cold surface. In order to make the simulation more realistic, the actual frost crystal nucleus deformation process is considered in this model. The simulation results agree well with our experimental results. Detailed analysis was made on the dynamic behavior of liquid-solid phase change and heat transfer happening in the frost crystal nucleation process. Results are presented for the evolution law of frost crystal nucleus deformation, dynamic solid-liquid phase change process as well as the dynamic distribution of frost nucleus interior temperature during frost crystal nucleation. In addition, the occurrence of frost crystal nucleus deformation is explained by the theory of crystal growth. Finally, where and why the initial position of frost crystal growth happens is also revealed. Furthermore, the reason why the hydrophobic surface can delay the droplet freezing and why the frost growth is faster on the hydrophobic surface after the droplet is frozen is analyzed based on this model.