We study the properties of acetic acid and propionic acid solutions at the surface of monocrystalline ice with surface-specific vibrational sum-frequency generation (VSFG) and heterodyne-detected vibrational sum-frequency generation spectroscopy (HD-VSFG). When we decrease the temperature toward the eutectic point of the acid solutions, we observe the formation of a freeze concentrated solution (FCS) of the carboxylic acids that is brought about by a freeze-induced phase separation (FIPS). The freeze concentrated solution freezes on top of the ice surface as we cool the system below the eutectic point. We find that for freeze concentrated acetic acid solutions the freezing causes a strong decrease of the VSFG signal, while for propionic acid an increase and a blue-shift are observed. This different behavior points at a distinct difference in molecular-scale behavior when cooling below the eutectic point. We find that cooling of the propionic acid solution below the eutectic point leads to the formation of hydrogen-bonded dimers with an opposite alignment of the carboxylic acid O-H groups.