The increasing adoption of Smart Grids brings about significant benefits such as enhanced efficiency and sustainability, but entails also severe threats to consumer privacy due to the possibility of establishing detailed user profiles. Existing efforts mostly focus on privacy issues in Smart Metering. However, the Smart Grid contains other important use cases whose privacy challenges have not received much attention to date. In this paper we aim to raise awareness for privacy issues in e-mobility, which will be a cornerstone application of the future Smart Grid. In particular, we study in detail the properties of privacy-relevant e-mobility use cases, the actors involved in those scenarios, and the data they exchange as part of their interaction. We investigate to which extent existing solutions can be applied to address emerging privacy challenges in e-mobility, and propose privacy-aware design patterns.