Where there's a thin layer of dirt on the ice, it looks like windblown dirt, and feels like you're on the moon. The surface of the glaciers is mottled grey because there is debris on the surface as well, though it is generally a thin layer of silt or scattered gravel, unlike the moraines which are true rock piles.
Continuing the glaciology lecture... There's a lot of debris trapped under and in the glacier also, and it all travels downhill with the glacier. If a glacier begins to melt faster than it flows downhill, it recedes. As the end, or terminus, melts, the trapped debris piles up and is left behind, forming the terminal moraine.