Like in the real world, perceptions of risk can influence the behavior and decisions that people make in online platforms. Users of Social Network Sites (SNSs) like Facebook make continuous decisions about their privacy since these are spaces designed to share private information with large and diverse audiences. In~particular, deciding whether or not to disclose such information will depend largely on each individual’s ability to assess the corresponding privacy risks. However, SNSs often lack awareness instruments that inform users about the consequences of unrestrained self-disclosure practices. Such an absence of risk information can lead to poor assessments and, consequently, undermine users' privacy behavior. This work elaborates on the use of risk scenarios as a strategy for promoting safer privacy decisions in SNSs. In particular, we investigate, through an online survey, the~effects of communicating those risks associated with online self-disclosure. Furthermore, we analyze the users' perceived severity of privacy threats and its importance for the definition of personalized risk awareness mechanisms. Based on our findings, we introduce the design of preventative nudges as an approach for providing individual privacy support and guidance in SNSs.