The impact and freezing of liquid droplets on cold surfaces can lead to ice formation on aircraft surfaces, posing a threat to flight safety. Due to its inherent complexity, simulating the impact and freezing process of liquid droplets is challenging. Additionally, limitations in experimental techniques make it difficult to replicate the conditions under which the environmental temperature is ultra-cold and the droplets are significantly supercooled in certain icing environments for aircraft. Therefore, the present work establishes a three-dimensional lattice Boltzmann method to simulate the impact freezing process of room-temperature and supercooled droplets on cold superhydrophobic surfaces. This model utilizes an enhanced cascaded lattice Boltzmann method alongside the multi-relaxation-time scheme to accurately solve the fluid flow and liquid-solid phase change model, with the accuracy validated by replicating experimental results. The influence of key factors such as Weber number, surface temperature, and droplet supercooling on the impact freezing process of droplets is also thoroughly investigated in this work.