When the temperature is well below 32F the sun melts a thin layer of snow. The droplets reach the cold edge of the roof and freeze. More droplets run down the accumulating ice and the icicle grows. The roof flat surface is warm, the free fall air at the roof edge is not.
The initial melting happens because the roof presents a flat face to the sun. Energy from 93,000,000 miles away is significant. The sun heats a flat surface but not the air. The air (scattered molecules with large space between) must gain energy from some warm surface.
