Internet of medical things (IoMT) is getting researchers' attention due to its wide applicability in healthcare. Smart healthcare sensors and IoT enabled medical devices exchange data and collaborate with other smart devices without human interaction to securely transmit collected sensitive healthcare data towards the server nodes. Alongside data communications, security and privacy is also quite challenging to securely aggregate and transmit healthcare data towards Fog and cloud servers. We explored the existing surveys to identify a gap in literature that a survey of fog-assisted secure healthcare data collection schemes is yet contributed in literature. This paper presents a survey of different data collection and secure transmission schemes where Fog computing based architectures are considered. A taxonomy is presented to categorize the schemes. Fog assisted smart city, smart vehicle and smart grids are also considered that achieve secure, efficient and reliable data collection with low computational cost and compression ratio. We present a summary of these scheme along with analytical discussion. Finally, a number of open research challenges are identified. Moreover, the schemes are explored to identify the challenges that are addressed in each scheme.