Soluble species induce surface premelting at the air-ice interface in the thermodynamic ice stability domain below the liquidus. This quasi-liquid layer is thought to increase in thickness with concentration of impurities and to represent a reservoir into which larger amounts of soluble species dissolve compared to a more rigid ice surface. To directly investigate the response of the quasi-liquid layer to increasing amounts of solutes and to clarify the distribution of these at the ice surface with depth, we use a combination of Auger electron yield X-ray absorption and photoelectron spectroscopies. We studied the adsorption of formic acid to ice at 251 K. These two complementary methods allow concluding that solutes enter the air-ice interface but do not necessarily induce a thicker quasi-liquid layer. Rather, modifications of the hydrogen-bonding network seem to be linked to the formation of solvation shells. We suggest that the flexibility of water molecules in the quasi-liquid layer is essential to form solvation shells and interpret the confinement of formic acid to the upper few ice bilayers to be linked with the structure of the hydrogen-bonding network getting more ice-like and rigid with depth at the air-ice interface.