The next generations of vehicles will require data transmission rates in the order of terabytes per driving hour, to support advanced automotive services. This unprecedented amount of data to be exchanged goes beyond the capabilities of existing communication technologies for vehicular communication and calls for new solutions. A possible answer to this growing demand for ultra-high transmission speeds can be found in the millimeter-wave (mmWave) bands which, however, are subject to high signal attenuation and challenging propagation characteristics. In particular, mmWave links are typically directional, to benefit from the resulting beamforming gain, and require precise alignment of the transmitter and the receiver beams, an operation which may increase the latency of the communication and lead to deafness due to beam misalignment. In this paper, we propose a stochastic model for characterizing the beam coverage and connectivity probability in mmWave automotive networks. The purpose is to exemplify some of the complex and interesting tradeoffs that have to be considered when designing solutions for vehicular scenarios based on mmWave links. The results show that the performance of the automotive nodes in highly mobile mmWave systems strictly depends on the specific environment in which the vehicles are deployed, and must account for several automotive-specific features such as the nodes speed, the beam alignment periodicity, the base stations density and the antenna geometry.