Health monitoring devices are gaining popularity both as wellness tools and as a source of information for healthcare decisions. In this work, we use Spiking Neural Networks (SNNs) for time-series forecasting due to their proven energy-saving capabilities. Thanks to their design that closely mimics the natural nervous system, SNNs are energy-efficient in contrast to classic Artificial Neural Networks (ANNs). We design and implement an energy-efficient privacy-preserving forecasting system on real-world health data streams using SNNs and compare it to a state-of-the-art system with Long short-term memory (LSTM) based prediction model. Our evaluation shows that SNNs tradeoff accuracy (2.2× greater error), to grant a smaller model (19% fewer parameters and 77% less memory consumption) and a 43% less training time. Our model is estimated to consume 3.36μJ energy, which is significantly less than the traditional ANNs. Finally, we apply ε-differential privacy for enhanced privacy guarantees on our federated learning-based models. With differential privacy of ε = 0.1, our experiments report an increase in the measured average error (RMSE) of only 25%.