We have investigated the interaction of n-butanol (NBA) with thin layers of water ice prepared in ultra high vacuum in the temperature range of 110-150 K. From the mass spectra of the chemically sputtered species, created upon the collision of low energy (>= 30 eV) Ar+ ions, we study the process of diffusive mixing of NBA with water ice, at the molecular level. The results show that NBA undergoes diffusive mixing with H2O. Even after depositing 1000 monolayers (MLs) of amorphous solid water (ASW) over NBA, both the species are observed on the surface. However, when NBA is deposited over ASW, no water is seen on the surface above 3-5 MLs of NBA. This could be interpreted as the absence of diffusive mixing in this system or surface segregation of NBA, in view of its lower surface energy just as in the case of liquid alcohols. An isomeric alcohol, namely, tert-butyl alcohol (TBA), also behaves similarly. Although the presence of NBA and TBA is detected, in the presence of ASW, they undergo selective ionization, giving specific peaks in the mass spectrum. D2O behaves in a manner similar to that of H2O. Preliminary experiments with other alcohols; namely, methanol, ethanol, and propanol were also done, and the results suggest that incomplete diffusion or surface segregation begins with propanol.