There is a consensus that future medicine will benefit from a comprehensive analysis of harmonized, interconnected, and interoperable health data. These data can originate from a variety of sources. In particular, data from veterinary diagnostics and the monitoring of health-related life parameters using the Internet of Medical Things are considered here. To foster the usage of collected data in this way, not only do technical aspects need to be addressed but so do organizational ones, and to this end, a socio-technical matrix is first presented that complements the literature. It is used in an exemplary analysis of the system. Such a socio-technical matrix is an interesting tool for analyzing the process of data sharing between actors in the system dependent on their social relations. With the help of such a socio-technical tool and using equine veterinary medicine as an example, the social system of veterinarians and owners as actors is explored in terms of barriers and enablers of an effective digital representation of the global equine population.