As we approach the exascale era, the size and complexity of HPC systems continues to increase, raising concerns about their manageability and sustainability. For this reason, more and more HPC centers are experimenting with fine-grained monitoring coupled with Operational Data Analytics (ODA) to optimize efficiency and effectiveness of system operations. However, while monitoring is a common reality in HPC, there is no well-stated and comprehensive list of requirements, nor matching frameworks, to support holistic and online ODA. This leads to insular ad-hoc solutions, each addressing only specific aspects of the problem. In this paper we propose Wintermute, a novel generic framework to enable online ODA on large-scale HPC installations. Its design is based on the results of a literature survey of common operational requirements. We implement Wintermute on top of the holistic DCDB monitoring system, offering a large variety of configuration options to accommodate the varying requirements of ODA applications. Moreover, Wintermute is based on a set of logical abstractions to ease the configuration of models at a large scale and maximize code re-use. We highlight Wintermute's flexibility through a series of practical case studies, each targeting a different aspect of the management of HPC systems, and then demonstrate the small resource footprint of our implementation.