Existing methods mainly handle single weather types. However, the connections of different weather conditions at deep representation level are usually ignored. These connections, if used properly, can generate complementary representations for each other to make up insufficient training data, obtaining positive performance gains and better generalization. In this paper, we focus on the very correlated rain and snow to explore their connections at deep representation level. Because sub-optimal connections may cause negative effect, another issue is that if rain and snow are handled in a multi-task learning way, how to find an optimal connection strategy to simultaneously improve deraining and desnowing performance. To build desired connection, we propose a smart knowledge assignment strategy, called SmartAssign, to optimally assign the knowledge learned from both tasks to a specific one. In order to further enhance the accuracy of knowledge assignment, we propose a novel knowledge contrast mechanism, so that the knowledge assigned to different tasks preserves better uniqueness. The inherited inductive biases usually limit the modelling ability of CNNs, we introduce a novel transformer block to constitute the backbone of our network to effectively combine long-range context dependency and local image details. Extensive experiments on seven benchmark datasets verify that proposed SmartAssign explores effective connection between rain and snow, and improves the performances of both deraining and desnowing apparently. The implementation code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/SmartAssign.