Human activity recognition plays a crucial role in enabling remote monitoring and assistive healthcare for older adults in smart home environments. However, traditional machine learning approaches often struggle to achieve high recognition accuracy without labeled data, while also preserving user privacy and protecting sensitive information. Although various studies have explored federated learning, effective models for human activity recognition using ambient sensors that simultaneously address privacy concerns and annotation scarcity remain limited. In this paper, we propose FedCSSL, a federated contrastive self-supervised learning framework based on the SimCLR architecture for human activity recognition using ambient sensor data. In our approach, each smart home (client) trains a local contrastive self-supervised model and periodically uploads its model weights to a central server. The server aggregates these weights using either the FedAvg or FedAdam algorithm and distributes the updated global model back to the clients for further training. We evaluated FedCSSL on four real-world smart homes within a residential community. The experiments involve three task scenarios and incremental scenarios to simulate real-world cold starts and knowledge transfer. The results demonstrate that FedCSSL effectively mitigates the annotation scarcity challenge by leveraging representations learned across smart homes without compromising privacy and security. The proposed framework has strong potential for broader application in smart home healthcare systems.