Infrared reflection-absorption spectroscopy has been used to characterize thin overlayers (1-200 Angstrom) of D2O ice deposited in UHV onto a set of self-assembled alkanethiolate monolayers (SAMs) of controlled wettabilities on gold. The SAMs were prepared from a series of controlled composition, mixed solutions of HS(CH2)(15)CH3 and HS(CH2)(16)OH, making it possible to investigate the whole wettability range from theta approximate to 0 degrees to theta=112 degrees, where theta is the static contact angle with water. Dosing of D2O and infrared measurements were carried out at selected sample temperatures between 82 and 150 K. Experimental spectra of ice overlayers recorded below 100 K on all SAM substrates are in good agreement with simulated reflection-absorption spectra, derived from the optical constants of amorphous ice. This agreement allows accurate film thickness determination. In contrast, lack of correspondence in spectral signature is noted between the spectra of annealed films and simulated polycrystalline (or amorphous) ice spectra. We interpret this discrepancy to suggest that significant substrate-induced differences between thin overlayers and bulk ice persist in the latter case. Spectral indications of ice-substrate interaction are also seen for amorphous ice, and are especially prominent in the case of highly hydrophobic (pure CH3-terminated, theta=112 degrees) substrates. In this case the substrate effect extends up to an average film thickness (150-200 Angstrom) corresponding to similar to 50 ice monolayers, in contrast to highly hydrophilic OH-terminated substrate, where the substrate effects appear to vanish beyond similar to 5 monolayers (15-20 Angstrom average thickness). Annealing of thin ice overlayers (2-3 monolayers) clearly demonstrates a strong correlation between the onset as well as progression of the transition from amorphous to polycrystalline ice and the exact substrate wettability or chemical composition. The data further suggest the existence of metastable intermediate forms, that are neither purely amorphous nor polycrystalline. We discuss these observations in terms of substrate-overlayer interaction. A tentative "phase diagram" summarizing these results is presented.