The adsorption of acetamide on low density amorphous (LDA) ice is investigated by grand canonical Monte Carlo computer simulations at the temperatures 50, 100, and 200 K, characteristic of certain domains of the interstellar medium (ISM). We found that the relative importance of the acetamide-acetamide H-bonds with respect to the acetamide-water ones increases with decreasing temperature. Thus, with decreasing temperature, the existence of the stable monolayer, characterizing the adsorption at 200 K, is gradually replaced by the occurrence of marked multilayer adsorption, preceding even the saturation of the first layer at 50 K. While isolated acetamide molecules prefer to lay parallel to the ice surface to maximize their H-bonding with the surface water molecules, this orientational preference undergoes a marked change upon saturation of the first layer due to increasing competition of the adsorbed molecules for H-bonds with water and to the possibility of their H-bond formation with each other. As a result, molecules stay preferentially perpendicular to the ice surface in the saturated monolayer. The chemical potential value corresponding to the point of condensation is found to decrease linearly with increasing temperature. We provide, in analogy with the Clausius-Clapeyron equation, a thermodynamic explanation of this behavior and estimate the molar entropy of condensed phase acetamide to be 34.0 J/mol K. For the surface concentration of the saturated monolayer, we obtain the value 9.1 ± 0.8 µmol/m2, while the heat of adsorption at infinitely low surface coverage is estimated to be -67.8 ± 3.0 kJ/mol. Our results indicate that the interstellar formation of peptide chains through acetamide molecules, occurring at the surface of LDA ice, might well be a plausible process in the cold (i.e., below 50 K) domains of the ISM; however, it is a rather unlikely scenario in its higher temperature (i.e., 100-200 K) domains.