The adsorption of acetone molecules on a proton ordered ice Ih(0001) surface was studied using classical molecular dynamics simulations between 50 and 150 K. At low coverage, we show that acetone molecules form an ordered monolayer on this ice surface, which is stable for T less than or equal to 100 K. At higher temperature, it exhibits orientational disordering, though local translational order remains. Preliminary simulations at higher coverage indicates the formation of additional ordered layers above the first monolayer, which are also stable below 100 K. These results support previous conclusions on the acetone/ice interactions based on the interpretation of experimental data.