Federated Learning (FL) has become a key method for preserving data privacy in Internet of Things (IoT) environments, as it trains Machine Learning (ML) models locally while transmitting only model updates. Despite this design, FL remains susceptible to threats such as model inversion and membership inference attacks, which can reveal private training data. Differential Privacy (DP) techniques are often introduced to mitigate these risks, but simply injecting DP noise into black-box ML models can compromise accuracy, particularly in dynamic IoT contexts, where continuous, lifelong learning leads to excessive noise accumulation. To address this challenge, we propose Federated HyperDimensional computing with Privacy-preserving (FedHDPrivacy), an eXplainable Artificial Intelligence (XAI) framework that integrates neuro-symbolic computing and DP. Unlike conventional approaches, FedHDPrivacy actively monitors the cumulative noise across learning rounds and adds only the additional noise required to satisfy privacy constraints. In a real-world application for monitoring manufacturing machining processes, FedHDPrivacy maintains high performance while surpassing standard FL frameworks - Federated Averaging (FedAvg), Federated Proximal (FedProx), Federated Normalized Averaging (FedNova), and Federated Optimization (FedOpt) - by up to 37%. Looking ahead, FedHDPrivacy offers a promising avenue for further enhancements, such as incorporating multimodal data fusion.