Connected devices using the internet, such as smart home appliances, wearable technology, and other IoT devices, keep becoming more prevalent in our daily lives. At the same time, privacy of the IoT is still a great concern, and consumers need better ways to understand privacy issues clearly. We provide an overview of smart home device privacy policies in the context of the EU area and particularly Finland. In the current study, we analyze the privacy policies of mobile applications associated with 20 smart home devices, and assess these documents in terms of clarity and transparency. We find that the policies are frequently very vague about the third-parties involved, and often fail to clearly indicate whether the privacy policy applies to a specific device model, several models, associated mobile application, or company website.