When I shoot on overcast days I get fantastic images. This week with sunlight its all wrong
The white balance function in digital capture is essentially a matter of adjusting the raw RGB values according to the colour temperature of the scene's illumination. As you say, on an overcast day this is no problem. The reason for this is that there is a single illumant: grey sky.
On a sunny day, however, there are two illuminants: the sun itself and the sky. When the sun is low its light is closer to the red end of the spectrum, which is in direct contrast to the blue of the sky. Shadow areas are those areas which are not
illuminated by the sun, so any photons we receive from them are either reflected off something sunlit (usually a small percentage) or come directly from the sky (usually the majority).*
If you were to use a colorimeter or a grey card in such a scene you would get one reading in the sunlight and another, very different, reading in the shadows. Even your visual cortex can't handle this: under these conditions you will see that snow actually looks blue-grey in shadows instead of pure grey. If you use the sunlit reading, that will turn the reddish light white while making the shadows even bluer; using the shadow-lit reading will have the opposite effect.
Artificially averaging the readings might produce something close to how the human brain would process the same scene. Just like the white balance of a digital camera, the visual cortex will attempt to rectify any illuminant, which is called white adaptation.**
So what to do? The technician's solution might be to use a colorimeter, then average the readings. But does the brain simplistically average the two extremes, or does it weight according to the percentage of the scene illuminated by each, or something else?
I'm just a poor artsy-fartsy type, so you won't get any brilliant technical solution from me. Instead, I can only suggest you do what I do: make a selection of the shadow areas of the scene in Photoshop, remove as much or as little of the blue cast as you like (or make it bluer!); then optionally invert the selection, then remove as much or as little of the warm cast as you like (or make it warmer).
Since you mentioned "artistic judgement", is is possible you are creating an image in your mind that is in fact not real.
which is not necessarily a bad thing.
I think we can see from the above that there is precious little about our perception of a scene that is
"real". The eye takes in photons then translates their vibratory frequencies into subjective colour experience according to sophisticated image processing techniques that includes white adaptation, edge contrast enhancement, etc. In fact, all colour is false colour. There is nothing intrinsically red about 700 nanometer vibrations or intrinsically violet about 400 nanometer vibrations: this is evolution's gift to us. I strongly feel that to the degree that one, as a photographer, is also an artist, one's task is not simply to create an acceptably realistic simulation of the recorded scene. One needs also to imbue that scene with emotional value. Every color has an emotional charge. A documenter attempts to record what he thinks
he saw when he looked at a scene. An artist attempts to convey what he wants you to feel
when you look at the scene he presents. For an artist, the question is not whether the colours are "accurate" (whatever that means), but whether they remain believable
while performing their primary task of orchestrating emotions.
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* There was a scientific paper on this subject that appeared on Outback Photo
last year, but I can't find it now.
** This is why a white wall viewed in tungsten light from indoors will look reasonably white, even though tungsten light is orangish; but if you go outside in the evening, then look in through a window at the same wall in the tungsten-lit room, it will look a livid yellow-orange.