On a sunny day, the light from the sky passes through the sky and lands on the earth. The horizontal ground plane is very bright. It is hard to look at. You have to squint. But, you can easily look at the blue part of the sky (not into the sun) because the light has passed through it.
On an overcast day, the light from the sky stays in the sky. The horizontal ground plane does not reflect a lot of light. You can easily look at it. However, you squint when you look at the sky because the light is still in it.
So, what does this mean? On a hazy day the sky is very bright and the ground plane has lower values than you would expect. It is a gray day, but there are still darks and accents. Don't mistake overcast for foggy. Those are two different situations. An overcast day can have dark shadow values. A foggy or misty day has dark values more in the middle value range.
Also, on a hazy day, the light source is cool. It is the sky and not the sun. The shadows have a lot of warmth in them. This morning the rose garden, the sky was very cool - and I saw crimsons and oranges in the foreground shadows. On a sunny day, the warm light from the sun overpowers the cool, secondary light from the sky - and the shadows appear cool in comparison.
Today, I didn't use an umbrella. I've learned my lesson. My paintings are darker than I thought. There was so much light in the sky, I could see colors very well in my painting. But, because of that light my eyes closed down. Indoors, the paintings look much darker and less colorful in the shadows. Oh, that dratted umbrella. It is a must.