Visible light communication (VLC) is considered to be a promising technology for realizing intelligent transportation systems (ITSs) and solving traffic safety problems. Due to the complex and changing environment and the influence of weather and other aspects, there are many problems in channel modeling and performance analysis of vehicular VLC. Unlike existing studies, this study proposes a practical vehicle-to-infrastructure (V2I) VLC propagation model for a typical mountain road. The model consists of both line-of-sight (LOS) and non-line-of-sight (NLOS) links. In the proposed model, the effects of vehicle mobility and weather conditions are considered. To analyze the impact of the considered propagation characteristics on the system, closed-form expressions for several performance metrics were derived, including average path loss, received power, channel capacity, and outage probability. Furthermore, to verify the accuracy of the derived theoretical expressions, simulation results were presented and analyzed in detail. The results indicate that, considering the LOS link and when the vehicle is 50 m away from the infrastructure, the difference in channel gain between moderate fog and dense fog versus clear weather conditions is 1.8 dB and 3 dB, respectively. In addition, the maximum difference in total received optical power between dense fog conditions and clear weather conditions can reach 76.2%. Moreover, under clear weather conditions, the channel capacity when vehicles are 40 m away from infrastructure is about 98.9% lower than when they are 10 m away. Additionally, the outage probability shows a high correlation with the threshold data transmission rate. Therefore, the considered propagation characteristics have a significant impact on the performance of V2I-VLC.