Image quality often deteriorates under challenging weather conditions such as haze and snow, which create significant barriers for vision-driven intelligent systems, including autonomous vehicles, real-time surveillance, and remote sensing applications. To address this pressing challenge, we propose a comprehensive deep learning framework capable of simultaneously handling both image dehazing and desnowing in a unified manner. At the core of our design lies the NAFXT block—an advanced extension of NAFNet—that integrates Dynamic Tanh (DyT) normalization in place of the traditional layer normalization. Notably, DyT normalization is introduced for the first time in this context as a more effective alternative, offering superior adaptability compared to standard layer normalization within convolutional neural network (CNN) architectures, particularly the NAFNet framework. While layer normalization primarily ensures stable training and faster convergence, DyT normalization enhances the model’s ability to capture richer and more expressive feature representations. As a result, the proposed framework achieves better restoration quality while requiring fewer training epochs than several cutting-edge methods. In addition, we incorporate the Multi-Branch Dynamic Selective Frequency (MDSF) and Multi-Branch Compact Selective Frequency (MCSF) modules, originally introduced in FSNet, to promote frequency-aware global feature learning across multiple scales. The network further adopts a multi-input and multi-output encoder–decoder structure, where both NAFXT and residual blocks are systematically integrated at every stage to progressively refine the restored outputs. Extensive experiments performed on three widely recognized benchmark datasets confirm that our method consistently surpasses state-of-the-art approaches, achieving higher quantitative scores and delivering visually sharper, clearer, and more natural results in both dehazing and desnowing tasks.