3D Clothing modeling and datasets play crucial role in the entertainment, animation, and digital fashion industries. Existing work often lacks detailed semantic understanding or uses synthetic datasets, lacking realism and personalization. To address this, we first introduce CloSe-D: a novel large-scale dataset containing 3D clothing segmentation of 3167 scans, covering a range of 18 distinct clothing classes. Additionally, we propose CloSe-Net, the first learning-based 3D clothing segmentation model for fine-grained segmentation from colored point clouds. CloSe-Net uses local point features, body-clothing correlation, and a garment-class and point features-based attention module, improving performance over baselines and prior work. The proposed attention module enables our model to learn appearance and geometry-dependent clothing prior from data. We further validate the efficacy of our approach by successfully segmenting publicly available datasets of people in clothing. We also introduce CloSe-T, a 3D interactive tool for refining segmentation labels. Combining the tool with CloSe-Net in a continual learning setup demonstrates improved generalization on real-world data.