An overcast day loses the direct light source of the sun and with it, most reflected light. When the sun is occluded by clouds or fog this leaves the scene with only ambient light or sky light. The difference is that this light is more neutral than on a sunny day when the color of this light is blue shifted from the sky color without clouds. In this type of lighting the objects have localized shadows and a tint from the cloud cover. Shadows tend to be warmer than they would be in full sunlight. The saying 'cool light warm shadows', applies here and can be used to great effect in this type of scene.
Color transitions are softer with subtle hue shifts and saturation shifts. Geometric planes are harder to discern. The direction for this light is top down as in most outdoor ambient light situations and the shadows have softer transitions. The lack of reflected light causes objects to darken in value toward their under planes continuously.
A full range of values is possible for overcast days but the light is shifted to the top planes and objects are dominated by local color with no strong light source to alter them. The light plane, upright plane and the shadow planes are closer together than they would be for objects in direct sunlight.
These kinds of days offer a longer period of time to paint from life because of the lack of a strong light source lessens the directional effect on shadows. More time allows for a more careful selection of the motif to maximize the pictures effectiveness as an overcast day painting.