Symmetry-adapted perturbation theory (SAPT) of three-body forces is applied to characterize the nonadditive interactions in the Ar-2-HF trimer. The origins of the anisotropy of the nonadditive Ar-2-HF potential are discussed, and the results are compared with the existing ab initio data. The multipole-expanded expressions for the induction, induction-dispersion, and dispersion nonadditivities in terms of the multipole moments and (hyper)polarizabilities are derived for the special case of atom-atom-diatom complexes, and the validity of the multipole approximation is investigated by comparison of the expanded and nonexpanded energies computed at the same level of the theory and in the same basis sets. Finally, recent (semi)empirical models of nonadditive interactions in Ar-2-HF based on the exchange quadrupole electrostatic interaction are analyzed in terms of contributions as defined by SAPT. It is shown that the present level of the SAPT theory correctly accounts for the terms included in the exchange quadrupole electrostatic model.