The adsorption of acetic acid on a proton-ordered water ice surface is modeled using periodic plane-waves density-functional theory. The structures of acetic acid adsorbed as a monomer or oligomers, hydrated or not, are calculated through gradient optimization. The resulting quantum electronic density of states are compared to metastable impact electron spectroscopy (MIES) results and lead to selection of the most plausible structures of acetic acid on water ice. Hypotheses are formulated for the structure of the acid film growing on the ice surface including mainly cyclic dimers and hydrated forms. Adsorptions of single water molecules on acetic acid crystal surfaces are also studied after optimization of the acetic acid crystal bulk and surface structure. More comparisons with spectroscopic studies are proposed in the accompanying paper.