Multi-weather image restoration has witnessed incredible progress, while the increasing model capacity and expensive data acquisition impair its applications in memory-limited devices. Data-free distillation provides an alternative for allowing to learn a lightweight student model from a pre-trained teacher model without relying on the original training data. The existing data-free learning methods mainly optimize the models with the pseudo data generated by GANs or the real data collected from the Internet. However, they inevitably suffer from the problems of unstable training or domain shifts with the original data. In this paper, we propose a novel Data-free Distillation with Degradation-prompt Diffusion framework for multi-weather Image Restoration (D4IR). It replaces GANs with pre-trained diffusion models to avoid model collapse and incorporates a degradation-aware prompt adapter to facilitate content-driven conditional diffusion for generating domain-related images. Specifically, a contrast-based degradation prompt adapter is firstly designed to capture degradation-aware prompts from web-collected degraded images. Then, the collected unpaired clean images are perturbed to latent features of stable diffusion, and conditioned with the degradation-aware prompts to synthesize new domain-related degraded images for knowledge distillation. Experiments illustrate that our proposal achieves comparable performance to the model distilled with original training data, and is even superior to other mainstream unsupervised methods.