Quantum satellite communication is an important part of global quantum secure communication network. In order to study the effect of snowfall on quantum satellite communication performance, first, based on the Gamma spectrum distribution function of snow particles and Mie scattering theory, the energy attenuation model of light quantum in snowfall environment is established. Then the relationship between the parameters such as snowfall intensity and the fidelity of the satellite-ground link, the channel establishment rate and the channel entanglement is studied, and the numerical simulation is carried out. Finally, in order to accurately simulate the impact of snow interference on the communication performance of satellite-ground links, a weighted noise channel model is introduced, and the impact of snow on the weighted noise channel capacity is analyzed. The results show that the snowfall intensity has a significant effect on the quantum energy and fidelity of light. When the transmission distance is 4.1 km and the snowfall intensity increases from 2.82 mm/d to 8.71 mm/d, the entanglement decreases from 0.738 to 0.206. When the snowfall intensity increases from 3.75mm/d to 8.25mm/d, the channel establishment rate decreases from 16.84 pair/s to 7.76 pair/s. When the transmission distance is 2.5km and the snowfall intensity increases from 4.0mm/d to 8.5mm/d, the weighted noise channel capacity decreases from 0.6207 to 0.3547. Therefore, the impact of snowfall on quantum satellite communication system cannot be ignored, and corresponding adjustment strategies should be taken to ensure the reliability and effectiveness of communication according to the snowfall level.