Edge intelligence is an emerging paradigm for real-time training and inference at the wireless edge, thus enabling mission-critical applications. Accordingly, base stations (BSs) and edge servers (ESs) need to be densely deployed, leading to huge deployment and operation costs, in particular the energy costs. In this article, we propose a new framework called Mobility-Enhanced Edge inTelligence (MEET), which exploits the sensing, communication, computing, and self-powering capabilities of intelligent connected vehicles for the smart and green 6G networks. Specifically, the operators can incorporate infrastructural vehicles as movable BSs or ESs, and schedule them in a more flexible way to align with the communication and computation traffic fluctuations. Meanwhile, the remaining compute resources of opportunistic vehicles are exploited for edge training and inference, where mobility can further enhance edge intelligence by bringing more compute resources, communication opportunities, and diverse data. In this way, the deployment and operation costs are spread over the vastly available vehicles, so that the edge intelligence is realized cost-effectively and sustainably. Furthermore, these vehicles can be either powered by renewable energy to reduce carbon emissions, or charged more flexibly during off-peak hours to cut electricity bills.