Unsupervised Domain Adaptation (UDA) for point cloud classification is an emerging research problem with relevant practical motivations. Reliance on multi-task learning to align features across domains has been the standard way to tackle it. In this paper, we take a different path and propose RefRec, the first approach to investigate pseudo-labels and self-training in UDA for point clouds. We present two main innovations to make self-training effective on 3D data: i) refinement of noisy pseudo-labels by matching shape descriptors that are learned by the unsupervised task of shape reconstruction on both domains; ii) a novel self-training protocol that learns domain-specific decision boundaries and reduces the negative impact of mislabelled target samples and in-domain intra-class variability. RefRec sets the new state of the art in both standard benchmarks used to test UDA for point cloud classification, showcasing the effectiveness of self-training for this important problem.