The importance of many-body effects in the hydration of the hydroxide ion (OH) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the CCSD(T) level of theory, extrapolated to the complete basis set limit, for the low-lying isomers of OH(HO) clusters, with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of OH and water molecules and the hydrogen bonding connectivity within each fragment. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) method, this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling OH hydration. Furthermore, the rapid convergence of the many-body expansion of the interaction energy also suggests a rigorous path for the development of analytical potential energy functions capable of describing individual OH-water many-body terms, with chemical accuracy. Finally, a comparison between the reference CCSD(T) many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that range-separated, dispersion-corrected, hybrid functionals exhibit the highest accuracy, while GGA functionals, with or without dispersion corrections, are inadequate to describe OH-water interactions.