Accurate environment maps are a key component to modelling real-world outdoor scenes. They enable captivating visual arts, immersive virtual reality and a wide range of scientific and engineering applications. To alleviate the burden of physical-capture, physically-simulation and volumetric rendering, sky-models have been proposed as fast, flexible, and cost-saving alternatives. In recent years, sky-models have been extended through deep learning to be more comprehensive and inclusive of cloud formations, but recent work has demonstrated these models fall short in faithfully recreating accurate and photorealistic natural skies. Particularly at higher resolutions, DNN sky-models struggle to accurately model the 14EV+ class-imbalanced solar region, resulting in poor visual quality and scenes illuminated with skewed light transmission, shadows and tones. In this work, we propose Icarus, an all-weather sky-model capable of learning the exposure range of Full Dynamic Range (FDR) physically captured outdoor imagery. Our model allows conditional generation of environment maps with intuitive user-positioning of solar and cloud formations, and extends on current state-of-the-art to enable user-controlled texturing of atmospheric formations. Through our evaluation, we demonstrate Icarus is interchangeable with FDR physically captured outdoor imagery or parametric sky-models, and illuminates scenes with unprecedented accuracy, photorealism, lighting directionality (shadows), and tones in Image Based Lightning (IBL).