Modern smart buildings and urban infrastructures increasingly depend on artificial intelligence to monitor, predict, and optimize energy performance. Deploying such intelligent systems across distributed devices and facilities requires approaches that are not only accurate and adaptive but also energy-efficient and privacy-preserving. Traditional centralized machine learning models are often less effective in this context, facing significant data privacy constraints and communication bottlenecks. Federated Learning (FL) provides a decentralized framework that allows multiple local agents, including smart meters, HVAC controllers, and building management nodes, to collaboratively train models without transmitting sensitive data to a central server. This study explores how FL can support lightweight decision and prediction models, including compact language or foundation models, designed for real-time energy monitoring and management. These models can operate efficiently on edge devices with limited computational power, a crucial requirement for widespread deployment. By emphasizing parameter-efficient and resource-aware learning, FL can reduce computational demands and communication costs, making continuous learning feasible within energy-constrained environments. This enables enhanced capabilities such as predictive maintenance scheduling, real-time load balancing, and personalized occupant comfort profiles. The integration of such distributed AI systems lays the foundation for intelligent, adaptive, and low-energy decision-support frameworks in sustainable buildings and urban infrastructures, advancing the vision of resilient and self-optimizing smart environments.