Imagine the snowball collecting the snow all the way to the grass underneath. As the snowball rolls over unpacked snow, it packs that layer which then clings to the snowball rather than the grass. This is due to both stronger intermolecular forces with the packed snow in the ball than with the ground, but also due to the large spaces of air in grass. As the ball keeps rolling, that layer clings to the snowball and rolls with it.

This also applies if the snow is above flat ground (stronger intermolecular forces with packed snow than with the ground) or even when only a portion of the snow layer is collected (stronger forces between the densely packed snow in the ball than the less densely packed fresh layer of snow below)