Motivated by recent experimental studies probing (i) the existence of a mobile layer at the free surface of glasses and (ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored, and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviors, over a temperature range typically bounded by the glass-transition temperature and the mode-coupling critical temperature. Layer-resolved analysis of the film particles' mean-squared displacements further shows that diffusion at the surface is considerably faster than in the bulk, below the glass-transition temperature. The diffusion coefficient of the surface particles is larger than its bulk counterpart by a factor that reaches 105 at the lowest temperature studied. This factor decreases upon heating, in agreement with recent experimental studies.