The phenomenon you are observing is called sublimation, which is the change from a solid state to a gas state without passing through a liquid state.
Let's say the temperature of the ice is 0 degrees C. This means the average temperature of all the molecules in the ice is at that temperature. However, the actual temperature of any individual molecule can be greater or less than the average. That means that some of the molecules are moving faster, and others slower, than the average.
Occasionally, some of the water molecules leave the surface of the ice on the windshield and are blown away by the moving wind. Since there is no way to supply more water molecules to the ice, it gradually gets smaller and smaller until it disappears.
Of course, a sunny day will make the process go faster as more molecules absorb energy from the sun and are able to escape their icy prison.
This same thing happens to comets as they get closer to the sun. See the link for more information.
As someone who has lived in the Nortern part of the United States, may I say that, having observed windshield ice on a personal level, ice will sometimes disappear from the windshield if it is not extremely thick and if the temperature outdoors is not much colder than the freezing point, and, especially, if the sun is out because the sunshine heats the windshield. In addition, if one drives his/her car with ice on the windshield, the heat from the engine may help to melt the ice. However, if there is ice on the windshield on a very cold day with no sunshine, this ice will not melt. When the wind chill is -20 degrees, for example, ice is not moving off.