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Satellite remote sensing (RS) has been drawing considerable research interest in land-cover classification due to its low price, short revisit time, and large coverage. However, clouds pose a significant challenge, occluding the objects on satellite RS images. In addition, snow coverage mapping plays a vital role in studying hydrology and climatology and investigating crop disease overwintering for smart agriculture. Distinguishing snow from clouds is challenging since they share similar color and reflection characteristics. Conventional approaches with manual thresholding and machine learning algorithms (e.g., SVM and Random Forest) could not fully extract useful information, while current deep-learning methods, e.g., CNNs or Transformer models, still have limitations in fully exploiting abundant spatial/spectral information of RS images. Therefore, this work aims to develop an efficient snow and cloud classification algorithm using satellite multispectral RS images. In particular, we propose an innovative algorithm entitled UCTNet by adopting a dual-flow structure to integrate information extracted via Transformer and CNN branches. Particularly, CNN and Transformer integration Module (CTIM) is designed to maximally integrate the information extracted via two branches. Meanwhile, Final Information Fusion Module and Auxiliary Information Fusion Head are designed for better performance. The four-band satellite multispectral RS dataset for snow coverage mapping is adopted for performance evaluation. Compared with previous methods (e.g., U-Net, Swin, and CSDNet), the experimental results show that the proposed UCTNet achieves the best performance in terms of accuracy (95.72%) and mean IoU score (91.21%) while with the smallest model size (3.93 M). The confirmed efficiency of UCTNet shows great potential for dual-flow architecture on snow and cloud classification. Full article