The freezing of water droplet is a ubiquitous phenomenon in nature. Although the freezing process of water droplet impacting on cold surfaces is widely observed on a macroscopic scale, the study of freezing process on a micro-scale is still deficient, and it is definitely difficult to study micro-droplets and nano-droplets using experimental methods due to the obstacles in both generation and observation. For these reasons, simulation methods using molecular dynamics (MD) have been proposed to study micro-droplets and nano-droplets, as molecular dynamics can trace each atom, count up the collective behavior of a group of atoms and describe the detail interaction between atoms. In this paper, a three-dimensional model is established by molecular dynamics simulation to study the freezing process of water droplets impinging on a cold solid surface on a nanoscale. We select the micro-canonical ensemble (NVE) as a statistical system and the TIP4P/ice model as a potential energy function to simulate oxygen atoms, hydrogen atoms and water molecules. The LJ/126 model is used to simulate the interaction between water molecules and solid atoms. Different wettability walls are simulated by adjusting the potential energy parameters. For all the simulations, the velocity-rescale method is used to keep the temperature constant and the Verlet algorithm is adopted to solve the Newton equations. In the velocity-rescale method, the temperature is calculated by using the profile-unbiased thermostat. The freezing process inside the water droplet is determined by the temperature distribution of water molecules along the vertical direction, which is more concise than by the location coordinates of the microscopic atoms. Through the numerical experimentations, we find that when the surface temperature decreases, the completely freezing time of drops is reduced; meanwhile, the time required for water temperature to drop down to the wall temperature is increased. Moreover, the heat transfer inside the water droplet slows down with the decreasing of wall hydrophilicity while the total freezing time is prolonged.