In$_2$O$_3$-based catalysts have shown high activity and selectivity for CO$_2$ hydrogenation to methanol, however the origin of the high performance of In$_2$O$_3$ is still unclear. To elucidate the initial steps of CO$_2$ hydrogenation over In$_2$O$_3$, we have combined X-ray Photoelectron Spectroscopy (XPS) and Density Functional Theory (DFT) calculations to study the adsorption of CO$_2$ on the In$_2$O$_3$(111) crystalline surface with different terminations, namely the stoichiometric, the reduced, and the hydroxylated surface, respectively. The combined approach confirms that the reduction of the surface results in the formation of In ad-atoms and that water dissociates on the surface at room temperature. A comparison of the experimental spectra and the computed core-level-shifts (using methanol and formic acid as benchmark molecules) suggests that CO$_2$ adsorbs as a carbonate on all surface terminations. We find that CO$_2$ adsorption is hindered by hydroxyl groups on the hydroxylated surface.