We carried out accurate diffusion Monte Carlo (DMC) studies for small (H2O)(N)X- clusters (N = 1-5; X- = F-, Cl-, Br-, I-) and their D2O isotopologues. We found remarkably good agreement (i.e., similar to 0.1 kcal/mol or better) with no exceptions between the DMC solvation energies and the corresponding harmonic approximation (HA) estimates, due, apparently, to massive error cancellations. This is surprising, in particular, because HA does not account for a substantial (i.e., similar to 3%) increase of the mean O-O distances, caused by the anharmonicity in conjunction with the nuclear quantum effects, although the other distances in the system are affected to a much lesser extent. This agreement for the solvation energies motivated us to extend the current study to larger (N = 6-21) clusters to explore their thermodynamic properties using the harmonic superposition method (HSM). The HSM results for the solvation free energies in turn reveal that at finite temperatures the nuclear quantum effects (including the isotope effects) in these systems are miniscule.