Recent realistic high resolution modeling studies show a net increase of submesoscale activity in fall and winter when the mixed layer depth is at its maximum. This submesoscale activity increase is associated with a reduced deepening of the mixed layer. Both phenomena can be related to the development of mixed layer instabilities, which convert available potential energy into submesoscale eddy kinetic energy and contribute to a fast restratification by slumping the horizontal density gradient in the mixed layer. In the present work, the mixed layer formation and restratification was studied by uniformly cooling a fully turbulent zonal jet in a periodic channel at different resolutions, from eddy resolving (10 km) to submesoscale permitting (2 km). The effect of the submesoscale activity, highlighted by these different horizontal resolutions, was quantified in terms of mixed layer depth, restratification rate and buoyancy fluxes. Contrary to many idealized studies focusing on the restratification phase only, this study addresses a continuous event of mixed layer formation followed by its complete restratification. The robustness of the present results was established by ensemble simulations. The results show that, at higher resolution, when submesoscale starts to be resolved, the mixed layer formed during the surface cooling is significantly shallower and the total restratification almost three times faster. Such differences between coarse and fine resolution models are consistent with the submesoscale upward buoyancy flux, which balances the convection during the formation phase and accelerates the restratification once the surface cooling is stopped. This submesoscale buoyancy flux is active even below the mixed layer. Our simulations show that mesoscale dynamics also cause restratification, but on longer time scales. Finally, the spatial distribution of the mixed layer depth is highly heterogeneous in the presence of submesoscale activity, prompting the question of whether it is possible to parameterize submesoscale effects and their effects on the marine biology as a function of a spatially-averaged mixed layer depth.