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Data privacy and eXplainable Artificial Intelligence (XAI) are two important aspects for modern Machine Learning systems. To enhance data privacy, recent machine learning models have been designed as a Federated Learning (FL) system. On top of that, additional privacy layers can be added, via Differential Privacy (DP). On the other hand, to improve explainability, ML must consider more interpretable approaches with reduced number of features and less complex internal architecture. In this context, this paper aims to achieve a machine learning (ML) model that combines enhanced data privacy with explainability. So, we propose a FL solution, called Federated EXplainable Trees with Differential Privacy (FEXT-DP), that: (i) is based on Decision Trees, since they are lightweight and have superior explainability than neural networks-based FL systems; (ii) provides additional layer of data privacy protection applying Differential Privacy (DP) to the Tree-Based model. However, there is a side effect adding DP: it harms the explainability of the system. So, this paper also presents the impact of DP protection on the explainability of the ML model. The carried out performance assessment shows improvements of FEXT-DP in terms of a faster training, i.e., numbers of rounds, Mean Squared Error and explainability.