Reconfigurable intelligent surfaces (RISs) empowered high-frequency (HF) wireless systems are expected to become the supporting pillar for several reliability and data rate hungry applications. Such systems are, however, sensitive to misalignment and atmospheric phenomena including turbulence. Most of the existing studies on the performance assessment of RIS-empowered wireless systems ignore the impact of the aforementioned phenomena. Motivated by this, the current contribution presents a theoretical framework for analyzing the performance of multi-RIS empowered HF wireless systems. More specifically, we statistically characterize the cascaded composite turbulence and misalignment channels in terms of probability density and cumulative distribution functions. Building upon the derived analytical expressions, we present novel closed-form formulas that quantify the joint impact of turbulence and misalignment on the outage performance for two scenarios of high interest namely cascaded multi-RIS-empowered free space optics (FSO) and terahertz (THz) wireless systems. In addition, we provide an insightful outage probability upper-bound for a third scenario that considers parallel multi-RIS-empowered FSO systems. Our results highlight the importance of accurately modeling both turbulence and misalignment when assessing the performance of such systems.