Deep learning based medical image segmentation has shown great potential in becoming a key part of the clinical analysis pipeline. However, many of these models rely on the assumption that the train and test data come from the same distribution. This means that such methods cannot guarantee high quality predictions when the source and target domains are dissimilar due to different acquisition protocols, or biases in patient cohorts. Recently, unsupervised domain adaptation techniques have shown great potential in alleviating this problem by minimizing the shift between the source and target distributions, without requiring the use of labeled data in the target domain. In this work, we aim to predict tissue segmentation maps on T2-weighted magnetic resonance imaging data of an unseen preterm-born neonatal population, which has both different acquisition parameters and population bias when compared to our training data. We achieve this by investigating two unsupervised domain adaptation techniques with the objective of finding the best solution for our problem. We compare the two methods with a baseline fully-supervised segmentation network and report our results in terms of Dice scores obtained on our source test dataset. Moreover, we analyse tissue volumes and cortical thickness measures of the harmonized data on a subset of the population matched for gestational age at birth and postmenstrual age at scan. Finally, we demonstrate the applicability of the harmonized cortical gray matter maps with an analysis comparing term and preterm-born neonates and a proof-of-principle investigation of the association between cortical thickness and a language outcome measure.