In the current work we examine the structural properties of water clusters that result from the hydration of a rigid H3O+ ion, under thermal conditions at T=250 K and for four different vapor pressures at 0.0156, 0.0625, 0.25, and 1 mbar. For this purpose we have constructed a model potential function that accounts explicitly not only for the three-body but for all orders of many-body interactions between the ion and the water molecules and for charge transfer effects as well. The adjustable parameters of the potential have been derived within similar to 0.1k(B)T accuracy through a concurrent fit to experimental enthalpy and entropy values from the corresponding cluster growth reactions. Many-body interactions have been found to comprise similar to 10% the three-body interactions, a fact that can not be ignored. The calculations have been carried out in the Grand Canonical ensemble (mu PT) where cluster sizes with a mean number of 6.69, 9.67, 29.17, and 44.37 water molecules for the four respective vapor pressures, have been generated. We have found a steady population transfer from the contact to the ion region to the second hydration shell as the vapor pressure increases. Typical equilibrium molecular configurations consist predominantly of pentagonal and hexagonal rings, that at p=1 mbar completely encircle the ion, forming in this way pronounced spherical cages. Radial distribution functions, polarization, and cluster density profiles have also been calculated.