While the adoption of connected vehicles is growing, security and privacy concerns are still the key barriers raised by society. These concerns mandate automakers and standardization groups to propose convenient solutions for privacy preservation. One of the main proposed solutions is the use of Pseudonym-Changing Strategies (PCSs). However, ETSI has recently published a technical report which highlights the absence of standardized and efficient PCSs [1]. This alarming situation mandates an innovative shift in the way that the privacy of end-users is protected during their journey. Software-Defined Networking (SDN) is emerging as a key 5G enabler to manage the network in a dynamic manner. SDN-enabled wireless networks are opening up new programmable and highly-flexible privacy-aware solutions. We exploit this paradigm to propose an innovative software-defined location privacy architecture for vehicular networks. The proposed architecture is context-aware, programmable, extensible, and able to encompass all existing and future pseudonym-changing strategies. To demonstrate the merit of our architecture, we consider a case study that involves four pseudonym-changing strategies, which we deploy over our architecture and compare with their static implementations. We also detail how the SDN controller dynamically switches between the strategies according to the context.