Acetic acid vapor-deposited on ultrathin noncrystalline ice (NCI) and polycrystalline ice (PCI) films (less than 6 nm thick) under ultrahigh vacuum conditions has been investigated by using Fourier Transform Infrared Reflection-Absorption Spectroscopy. Pristine acetic acid deposited at 123 K (on a copper support) appears as an amorphous solid, which undergoes an irreversible phase transformation to a more structurally ordered (polycrystalline) form upon annealing to 153 K. Acetic acid is found to adsorb on NCI and PCI films initially through hydrogen bonding between C=O and dangling OH (of ice), followed by the formation of multilayers at 123 K. Thermal evolution studies of a low exposure of acetic acid on the ultrathin NCI and PCI films show that acetic acid undergoes coevaporation with water likely as an acetic acid hydrate at 155 K, which continues until the entire ice film has been exhausted at 165 K. Above 165 K, the remaining acetic acid solid appears to evaporate without undergoing the phase transformation, in contrast to the case of a high acetic acid exposure. Coevaporation of acetic acid with water is also found to proceed at a faster rate than the subsequent evaporation of acetic acid, which is consistent with the weaker interactions observed in the H-bonded acetic acid hydrate than that in acetic acid solid.