Cloud Computing technologies and cloud-based Geographic Information Systems have became widely used in recent decades. However, the complexity and size of geospatial datasets remains growing and sometimes become going out of the cloud infrastructure paradigm. Additionally, many of currently used client devices have sufficient computational resources to store and process some amounts of data directly. Consequently, multilevel management techniques are demanded that support capabilities of horizontal (client-to-client) data flows in addition to vertical (cloud-to-client) data flows. These tendencies in information technologies (in general) have led to the appearance of Fog Computing paradigm that extends a cloud infrastructure with the computational resources of client devices and implements client-side data storage, management and interchange. This position paper summarizes and discusses mentioned tendencies in connection with a number of available Open Geospatial Consortium standards. The paper highlights the standards, which can be recognized as the platform for the Fog Computing implementation into geospatial domain, and analyzing their strong and weak features from the Fog Computing point of view. The analysis is built upon author's experience in implementation of the client-side geospatial Web services.