It is shown that a concise model potential can well account for the ground vibrational state rotational constants of Ar1-4HF clusters, the HF vibrational frequency shift of Ar1-4HF clusters, and the vibrational frequency shift of HF in an argon matrix. The model potential explicitly incorporates direct intermolecular polarization, which is a significant contributor to the stabilities of the clusters. Direct polarization produces an Ar-HF interaction that is different for HF in its ground vibrational state and its first excited vibrational state. That difference in interaction accounts for a sizable share of the HF red-shift for Ar clusters of all sizes. The calculations include full treatment of vibrational dynamics via quantum Monte Carlo for the ArnHF clusters with n = 1-12, and these show small effects of weak mode vibrations on the HF rid-shift. Calculations of the fully optimized equilibrium structures for n = 1-176 clusters plus calculations with optimized lattice structures of four, five, six, and seven solvation shells (through n > 2000) were used for extrapolation to an infinite cluster limit value for the HF red-shift. The second solvation shell is found to be noticeably important in the matrix red-shift. Three-body dispersion in the model potential has a direct effect on the red-shifts in large clusters, but the indirect effect via the influence on Ar-Ar separation is small.