In this work we investigate the effects of the environment on the X-ray photoelectron spectra of hydrogen chloride and the chloride ions adsorbed on ice surfaces, as well as of chloride ions in water droplets. In our approach, we combine a density functional theory (DFT) description of the ice surface with that of the halogen species with the recently developed relativistic core-valence separation equation of motion coupled cluster (CVS-EOM-IP-CCSD) via the frozen density embedding formalism (FDE), to determine the K and L_1,2,3 edges of chlorine. Our calculations, which incorporate temperature effects through snapshots from classical molecular dynamics simulations, are shown to reproduce experimental trends in the change of the core binding energies for Cl^- upon moving from a liquid (water droplets) to an interfacial (ice quasi-liquid layer) environment, and between Cl^- and HCl at the interface. Our simulations yield water valence band binding energies in good agreement with experiment, and that vary little between the droplets and the ice surface. For the halide core binding energies there is an overall trend of overestimating experimental values, though good agreement between theory and experiment is found for Cl^- in water droplets and on ice. For HCl there are significant discrepancies between experimental and calculated core binding energies, which we trace back to the inadequacy of the structural models employed to represent configurations in which pre-dissociation of HCl at the interface is taking place.