Variational calculations of vibrational energies, rotational constants and angular expectation values are carried out for the trimers Ar-2-HCl, Ar-2-DCl, Ar-2-HF and Ar-2-DF. Calculations are performed on pairwise additive potential energy surfaces and on surfaces including a variety of non-additive contributions. Attention is focused on the bending levels corresponding to hindered internal rotation of the HX molecule in the complex, several of which have been observed by high-resolution spectroscopy. The results confirm that it is crucial to include dispersion, induction and short-range effects when modelling the non-additive forces in molecular systems. It is found that the model of non-additive forces previously proposed by Ernesti and Hutson [Phys. Rev. A 51, 239 (1995)] works well for the bending bands of Ar-2-HCl, Ar-2-DCl and Ar-2-DF as well as Ar-2-HF. In addition, a new distributed model of the non-additive dispersion energy is proposed, in which the triple-dipole energy is partitioned between two anisotropic sites in the HX molecule.