This paper investigates the effects of three weather conditions, such as rain, snow, and haze, on security key rate of a free-space quantum communication system using different signal wavelengths. For the cases of collective and individual attacks, analysis is conducted on why and how different weather conditions and signal wavelengths affect the security key rate based on a continuous-variable quantum key distribution model with Gaussian modulation. In the analysis, two different conditions are considered: one in which Bob uses a homodyne detector and the other in which a heterodyne detector is used. The relationship between the security key rate and transmission distance is simulated under various conditions, including different weather conditions and levels, different quantum signal wavelengths, different attack types, and different detection modes. The results of this paper can serve as an instructive reference for future practical free-space quantum communication system designs.