The effect of the solvent, modeled as a hard sphere fluid, on the behavior of the double layer at low temperatures is studied by means of Monte Carlo simulations. We find that the density profiles are strongly affected by the addition of solvent molecules. The profiles pass from near monotonic functions that exhibit partial drying to oscillatory functions that exhibit partial wetting as the bulk density of the solvent is increased in the system. However, the capacitance, as in the case of the primitive model, increases at low effective temperatures, while after a maximum it decreases at higher effective temperatures as the temperature increases. We find that the adsorption of the ions decreases and changes sign from positive to negative with the decreasing temperature at low electrode charges. Some of these features can be explained by means of a contact value theorem.