Images captured in snowy days suffer from noticeable degradation of scene visibility, which degenerates the performance of current vision-based intelligent systems. Removing snow from images thus is an important topic in computer vision. In this paper, we propose a Deep Dense Multi-Scale Network (DDMSNet) for snow removal by exploiting semantic and depth priors. As images captured in outdoor often share similar scenes and their visibility varies with depth from camera, such semantic and depth information provides a strong prior for snowy image restoration. We incorporate the semantic and depth maps as input and learn the semantic-aware and geometry-aware representation to remove snow. In particular, we first create a coarse network to remove snow from the input images. Then, the coarsely desnowed images are fed into another network to obtain the semantic and depth labels. Finally, we design a DDMSNet to learn semantic-aware and geometry-aware representation via a self-attention mechanism to produce the final clean images. Experiments evaluated on public synthetic and real-world snowy images verify the superiority of the proposed method, offering better results both quantitatively and qualitatively. https://github.com/HDCVLab/Deep-Dense-Multi-scale-Network https://github.com/HDCVLab/Deep-Dense-Multi-scale-Network.