In the realm of precision medicine, effective patient stratification and disease subtyping demand innovative methodologies tailored for multi-omics data. Clustering techniques applied to multi-omics data have become instrumental in identifying distinct subgroups of patients, enabling a finer-grained understanding of disease variability. Meanwhile, clinical datasets are often small and must be aggregated from multiple hospitals. Online data sharing, however, is seen as a significant challenge due to privacy concerns, potentially impeding big data's role in medical advancements using machine learning. This work establishes a powerful framework for advancing precision medicine through unsupervised random forest-based clustering in combination with federated computing. We introduce a novel multi-omics clustering approach utilizing unsupervised random forests. The unsupervised nature of the random forest enables the determination of cluster-specific feature importance, unraveling key molecular contributors to distinct patient groups. Our methodology is designed for federated execution, a crucial aspect in the medical domain where privacy concerns are paramount. We have validated our approach on machine learning benchmark datasets as well as on cancer data from The Cancer Genome Atlas. Our method is competitive with the state-of-the-art in terms of disease subtyping, but at the same time substantially improves the cluster interpretability. Experiments indicate that local clustering performance can be improved through federated computing. The proposed methods are available as an R-package (https://github.com/pievos101/uRF).