The low temperatures and high resolution associated with helium droplet spectroscopy are used to obtain vibrational spectra for clusters containing a single HF molecule, surrounded by multiple H-2, D-2, and HD molecules. For clusters with fewer than nine HD molecules, the asymmetric solvent environment experienced by the HF prevents it from internally rotating. The results suggest that, for n = 9 and larger, the solvent cage becomes highly isotropic, allowing the HF molecule to undergo nearly free rotation. For H-2 and D-2 the mixture of ortho and para species in the clusters makes the solvent cage anisotropic even when the first solvent shell is complete and free rotation of the HF molecule is not observed.