We analyze the layering structure for the free liquid surface observed at low temperature in simple fluid models, with pair interaction potentials. The relationship of the surface layers with the Fisher-Widom line is discussed, by direct comparison of Monte Carlo simulation results for the liquid-vapor density profiles and the pair distribution function of the bulk liquid. Also we study the role of the capillary waves in the damping of the surface oscillatory profiles, with Monte Carlo simulations for different transverse areas, and through the theoretical scaling forms using the values of the surface tension given by our simulations. The main conclusion is that the dependence of the surface layering with the temperature is dominated by the capillary waves, even at the small transverse sizes typically used in computer simulations. In contrast, the Fisher-Widom line seems to be of minor importance for the amplitude of the layering.