When the day is cloudy, we think of the day as sunless when, actually, there is sunlight even though we cannot see the sun. Some light is passing through the clouds, but there is still plenty of light to see by. Likewise, a cloudy sky blocks some of the sun's heat from reaching the ground. Just as with sunlight, however, some of this infrared radiation from the sun also manages to pass through the clouds.
This is why ice and snow will often at least partially melt off streets and sidewalks exposed to the sky even on cloudy days that are below freezing. Of course, when the weather gets colder and afternoon temps are in the teens or lower, most of this daytime melting will stop. By late February and March, as the sun starts to get higher in the sky, the more direct solar radiation will cause melting even at very cold temperatures and even on cloudy days.