The snowmelt process plays a crucial role in hydrological forecasting, climate change, disaster management, and other related fields. Accurate detection of wet snow distribution and its changes is essential for understanding and modeling the snow melting process. To address the limitations of conventional fixed-threshold methods, which suffer from poor adaptability and significant interference from scattering noise, we propose a weakly supervised deep learning change detection algorithm with Sentinel-1 multi-temporal data. This algorithm incorporates the Multi-Region Convolution Module (MRC) to enhance the central region while effectively suppressing edge noise. Furthermore, it integrates the ResNet residual network to capture deeper image features, facilitating wet snow identification through feature fusion. Various combinations of differential images, polarization data, elevation, and slope information during and after snowmelt were input into the model and tested. The results suggest that the combination of differential images, VV polarization data, and slope information has greater advantages in wet snow extraction. Comparisons between our method, the fixed-threshold method, OTSU algorithm, and FCM algorithm against the results of Landsat images indicates that the overall accuracy of our method improves significantly when the proportion of wet snow cover is large, and the average overall accuracy of wet snow extraction is 85.2%. This study provides clues for the accurate identification of wet snow during the mid-snowmelt phase.