Foundation models (FMs) emerge as a promising solution to harness distributed and diverse environmental data by leveraging prior knowledge to understand the complicated temporal and spatial correlations within heterogeneous datasets. Unlike distributed learning frameworks such as federated learning, which often struggle with multimodal data, FMs can transform diverse inputs into embeddings. This process facilitates the integration of information from various modalities and the application of prior learning to new domains. However, deploying FMs in resource-constrained edge systems poses significant challenges. To this end, we introduce CoRAST, a novel learning framework that utilizes FMs for enhanced analysis of distributed, correlated heterogeneous data. Utilizing a server-based FM, CoRAST can exploit existing environment information to extract temporal, spatial, and cross-modal correlations among sensor data. This enables CoRAST to offer context-aware insights for localized client tasks through FM-powered global representation learning. Our evaluation on real-world weather dataset demonstrates CoRAST's ability to exploit correlated heterogeneous data through environmental representation learning to reduce the forecast errors by up to 50.3% compared to the baselines.