Snowfall severely degrades outdoor video visibility while reducing the performance of subsequent vision tasks. Although video recovery methods based on deep learning have achieved amazing accomplishments, video snow removal still faces problems such as varying scales and intricate trajectories of snowflakes, which makes it difficult to remove snowflakes and easy to create artifacts on moving objects. To address these issues, we propose a deformable multi-scale video desnowing network. Specifically, we design a multi-scale pseudo-3D residual block(MSRB-P3D) that can effectively remove snowflakes of different scales. Furthermore, a deformable large kernel attention 3Dblock(D-LKA 3Dblock) is introduced to capture the inter-frame dynamic information and reduce the artifacts. Due to the scarcity of dataset, we proposed a new dataset named Synthetic and Real Snowy Video Dataset(SRSVD). Extensive experiments have proven that our proposed method not only outperforms other state-of-the-art methods on both synthetic and real snowy videos, but also effectively improves performance on subsequent vision task.