Light emitting diodes (LEDs) are increasingly used in automotive exterior lighting. The expected wide availability of LED-based front and back lights makes visible light communication (VLC) a natural vehicular connectivity solution. A major challenge in vehicular VLC systems is their relatively poor performance in adverse weather conditions such as severe fog. In this paper, we propose the use of single-photon avalanche diode (SPAD) for vehicular VLC systems. With their higher sensitivity in comparison to conventional photodetectors, SPADs can be efficiently used to detect weak signals. Under the assumption of on-off keying (OOK), we present the error rate performance of vehicular VLC systems. Since the SPAD output is modelled by Poisson statistics, the bit error rate (BER) takes the form of a semi-infinite summation. Based on Anscombe transformation, we approximate Poisson noise as Gaussian and derive a closed-form BER expression. Using this expression, we obtain a closed-form expression for maximum achievable link distance to ensure a targeted BER. We present an extensive numerical study to validate our derivations and demonstrate the performance of vehicular VLC system under different weather conditions.