We study the behavior of sea ice under varying amounts of snow precipitation. We find that for the same external forcing, sea ice that forms in open water can grow substantially thicker than sea ice that survived a certain summer. This behavior is due to nonlinear effects of the insulating snow cover on the ice slab, constituting a snow-growth feedback. Moreover, we find the maximum thickness of first year sea ice to depend nonlinearly and nonmonotonically on the time of its initial formation if snow precipitation is present. We compare these effects to other feedbacks in sea ice like the ice-albedo feedback and the growth-thickness feedback. We also discuss the significance of these findings for the future evolution of sea-ice extent in the Arctic.