Polycyclic Aromatic Hydrocarbons (PAHs) are a family of molecules which represent the best candidates to explain the observation of one set of features in the Interstellar Medium (ISM): the Aromatic Interstellar Bands (AIBs). They could also contribute to the Diffuse Interstellar Bands (DIBs). In dense molecular clouds, PAHs may condense onto interstellar grains, contributing to the complex chemistry occurring in their icy mantles, composed essentially of water. In this context, the adsorption of various aromatic molecules, from benzene to ovalene, on different ices-both amorphous and crystalline-is investigated by means of classical molecular dynamics simulations. Initially, a systematic parametrization of the electronic charges on the chosen PAHs in these environments is carried out, and benchmarked with reference to free energies of solvation in liquid water. Then we propose a new, rigorous methodology, transferable to any other PAH or molecular species, to evaluate the charges to be applied to the molecule in the gas phase, at interfaces, or in liquid water. Ultimately, the adsorption energies calculated for the various PAHs are used to derive a function predicting the adsorption energy of any PAH on a given ice surface as a function of the number of C and H atoms it contains. For all PAHs studied, the largest adsorption energies are found on the crystalline hexagonal ice surface (Ih). Binding energy maps constructed for each PAH-ice pair give valuable insight into adsorption site densities and the barriers to surface diffusion. One key result is that the amorphous surface offers a smaller number of adsorption sites compared to that of hexagonal ice. A direct correlation between the location of energetically favourable adsorption sites and the presence of dangling H-bonds is also demonstrated using these maps, showing that PAHs adsorb preferentially on sites offering dangling H-bonds. The present work represents a complete description of PAH-ice interaction in the ground electronic state and at low temperature, providing the binding energies and barrier heights necessary to the ongoing improvement of astrochemical models.