Vehicle platooning is a promising technique to enhance travel safety and road capacity. A common form of platooning is Cooperative Adaptive Cruise Control (CACC), where cars communicate their states with each other to maintain a constant gap between them. CACC can further reduce the headway between adjacent vehicles. However, the frequently broadcast safety messages with precise location and time information impose a significant threat to the location privacy of cars. Mix-zone based approaches are traditionally used to obfuscate vehicles' identities by mixing their pseudonyms. However, vehicles' movement is tightly coupled with each other inside a vehicular platoon, which introduces high predictability and spatial-temporal correlation for trajectories of vehicles. In this paper, we show how an adversary can exploit vehicles' platooning states to better infer their pseudonyms by observing their broadcast states before and after entering a mix-zone. We propose a novel attack strategy using a maximum likelihood estimator and expectation-maximization algorithm, and demonstrate the effectiveness of this attack through extensive simulations based on the real data from U.S. Highway 101. Our strategy achieves 30% higher inference accuracy compared with traditional non-platooning traffic scenarios. We also suggest a few possible approaches to mitigate such privacy threat in a platooning environment.