Because photovoltaic (PV) solar systems use the full spectrum of light, the ultraviolet rays are still charging the system, even when the sunlight isn’t visible. Obviously, the system will produce more power on bright sunny days. In the event of a light snowfall, the snow should quickly melt and slide down the slanted face of the panel. (During Hurricane Sandy, we observed a PV installation in Southern New Jersey producing low levels of power until shortly before the storm made landfall. Incidentally, the panels were undamaged, despite being 30 miles from the storm’s eye.)
Most systems like this are designed so that they shut down when the power from the utility goes down. This is done for safety reasons, in order to prevent shocks and hazards to workers who are getting the utility lines back up and running.