The segmentation of individual trees from forest point clouds is a crucial task for downstream analyses such as carbon sequestration estimation. Recently, deep-learning-based methods have been proposed which show the potential of learning to segment trees. Since these methods are trained in a supervised way, the question arises how general models can be obtained that are applicable across a wide range of settings. So far, training has been mainly conducted with data from one specific laser scanning type and for specific types of forests. In this work, we train one segmentation model under various conditions, using seven diverse datasets found in literature, to gain insights into the generalization capabilities under domain-shift. Our results suggest that a generalization from coniferous dominated sparse point clouds to deciduous dominated high-resolution point clouds is possible. However, to obtain strong general segmentation models diverse training data from different laser scanners and forest types is necessary. To contribute to a more diverse data basis for model development, labeled trees from two previous works were adapted to the complete forest point cloud and are made publicly available.