Machine learning models often struggle with generalization in small, heterogeneous datasets due to domain shifts caused by variations in data collection and population differences. This challenge is particularly pronounced in biological data, where data is high-dimensional, small-scale, and decentralized across institutions. While federated domain adaptation methods (FDA) aim to address these challenges, most existing approaches rely on deep learning and focus on classification tasks, making them unsuitable for small-scale, high-dimensional applications. In this work, we propose freda, a privacy-preserving federated method for unsupervised domain adaptation in regression tasks. Unlike deep learning-based FDA approaches, freda is the first method to enable the federated training of Gaussian Processes to model complex feature relationships while ensuring complete data privacy through randomized encoding and secure aggregation. This allows for effective domain adaptation without direct access to raw data, making it well-suited for applications involving high-dimensional, heterogeneous datasets. We evaluate freda on the challenging task of age prediction from DNA methylation data, demonstrating that it achieves performance comparable to the centralized state-of-the-art method while preserving complete data privacy.