Albeit providing many benefits, smart homes collect and process large amounts of sensitive data. In order to successfully cope with the resulting risks for their privacy, users have to be aware of potential privacy threats and consequences in the first place. Since research in other contexts has shown that users often lack this awareness even when it comes to well-known technologies, e.g., Online Social Networks (OSN), it is crucial to investigate users' awareness of threats related to the use of unfamiliar technologies like smart homes. To this end, we conducted a survey study with 1052 lay users. By prompting participants to state all consequences that could potentially result from using smart home and smart health devices as well as OSN, we find that most participants were unable to state a single privacy consequence. Instead, most referred to general privacy issues (e.g., profiling, data collection) or threats related to non-privacy topics, such as security problems resulting from defect smart home devices. Since our participants were least aware of potential privacy consequences resulting from the use of smart home devices, further effort is necessary to inform lay users about possible privacy threats, e.g., by launching public campaigns or conducting trainings and interventions directly implemented in the UIs of smart home systems.