Exploring the freezing process and its potential mechanism of the droplets impacting on a solid surface is desperately desired, owing to its anti-icing applications in aircraft, cable, radar, etc. On the controllable low temperature test equipment, the freezing dynamic behaviors of droplets impacting on three cold plates, made of copper, aluminum and silicon, are recorded by a high-speed camera in this paper, and characterized by the droplet spreading diameter, oscillation and freezing time. Here, the freezing behavior of droplets is predicated by observing the color change of the droplet. Through the experimental exploration and theoretical analysis, we reveal the effects of the impacting speed, surface temperature and thermal conductivity of material on the freezing dynamics of the droplet. We demonstrate that a cold surface shrinks the maximum spreading diameter of droplet compared with the surface at ambient temperature; the lower the surface temperature, the shorter the freezing time would be and the smaller the maximum spreading diameter would be; the maximum spreading diameter increases with increasing Weber number, whereas the oscillation and freezing time decrease. Meanwhile, the higher the material thermal conductivity, the shorter the freezing time would be, and the bigger the rising slope of the maximum spreading diameter with increasing Weber number will be. A function to predict the freezing time is derived from thermodynamic condition. The calculated values are in good agreement with the experimental data, with the maximum relative error of less than 5.3%.