The demand for safe and secure journeys over roads and highways has been growing at a tremendous pace over recent decades. At the same time, the smart city paradigm has emerged to improve citizens' quality of life by developing the concept. Vehicular Ad hoc NETworks (VANETs) are widely recognized to be instrumental in realizing such concept, by enabling appealing safety and infotainment services. Such networks come with their own set of challenges, which range from managing high node mobility to securing data and user privacy. The Software Defined Networking (SDN) paradigm has been identified as a suitable solution for dealing with the dynamic network environment, the increased number of connected devices, and the heterogeneity of applications. While some preliminary investigations have been already conducted to check the applicability of the SDN paradigm to VANETs, and its presumed benefits for managing resources and mobility, it is still unclear what impact SDN will have on security and privacy. Security is a relevant issue in VANETs, because of the impact that threats can have on drivers' behavior and quality of life. This paper opens a discussion on the security threats that future SDN-enabled VANETs will have to face, and investigates how SDN could be beneficial in building new countermeasures. The analysis is conducted in real use cases (smart parking, smart grid of electric vehicles, platooning, and emergency services), which are expected to be among the vehicular applications that will most benefit from introducing an SDN architecture.