Various weather modelling problems (e.g., weather forecasting, optimizing turbine placements, etc.) require ample access to high-resolution, highly accurate wind data. Acquiring such high-resolution wind data, however, remains a challenging and expensive endeavour. Traditional reconstruction approaches are typically either cost-effective or accurate, but not both. Deep learning methods, including diffusion models, have been proposed to resolve this trade-off by leveraging advances in natural image super-resolution. Wind data, however, is distinct from natural images, and wind super-resolvers often use upwards of 10 input channels, significantly more than the usual 3-channel RGB inputs in natural images. To better leverage a large number of conditioning variables in diffusion models, we present a generalization of classifier-free guidance (CFG) to multiple conditioning inputs. Our novel composite classifier-free guidance (CCFG) can be dropped into any pre-trained diffusion model trained with standard CFG dropout. We demonstrate that CCFG outputs are higher-fidelity than those from CFG on wind super-resolution tasks. We present WindDM, a diffusion model trained for industrial-scale wind dynamics reconstruction and leveraging CCFG. WindDM achieves state-of-the-art reconstruction quality among deep learning models and costs up to $1000\times$ less than classical methods.