Shadows

Our brains sometimes fool us into thinking that shadows are grey.
This probably comes from what we were told in childhood.
For many people this prevents them from seeing the true colour of shadows.
One way to overcome this is to study a photograph that has clear shadows. Although photos often don't show all colours as true colours, they are nevertheless helpful in showing the effects created by shadows and overcoming the mental 'grey' block.

Just study the photo below.
Practice looking at real life shadows to 'learn' how to see the colours.

Shadow colours are clearly visible on this photograph of a lily.
Notice how the shadows take on the colours of the parts of the flower next to the shadow as the object colour is reflected into the shadow.
Also notice the relative tone of the shadow compared with the white card. Cast shadows are more than 5 tones darker than the sunlit object on a scale of 1 = White to 10 = black.

This colour and tonal strength can be used in a painting to give vibrancy to shadows.

The photograph was taken in bright sunlight with the lily on a white card.

Shadows in the landscape

Daylight colours - bright sunlight:

Shadow colour when it has no influence from reflected light from other objects is only lit by the blue light from the sky. The colour in the sky comes from sunlight being scattered by the molecules in the atmosphere.  
The colour from the sky in the shadow is modified by the particles in the atmosphere that it travels through, usually making it slightly warmer (towards purple) than the blue of the sky. So, a blue that leans towards purple, is the natural shadow colour that would be seen on a white surface on bright sunlit day.
The light from the sun, when high, is predominantly white. This directly lights things not in shadow.

Other outdoor conditions:

These colours can change depending on the condition and colour of the sky, the time of day and the place on earth that you are. The amount of atmosphere through which the light travels varies depending on the angle of the suns rays at different parts on the globe.
 

When painting the effect:

Wet in wet is a good choice for painting the colour variations in shadows as this give a gradual change from one colour to the next.

On a bright sunny day the colour of the shadow is the blue of the sky (whatever blue that is) plus some red. e.g. if its an Ultramarine sky the shadow is Ultramarine plus Permanent Alizarin Crimson or similar.

If the shadow falls on grass for example, adding this purple mix as a glaze on top of the grass colour will darken it, make it bluer and duller. It's best to use pigments that are transparent to ensure that the original, sunlit colour shows through.

Some artists start by painting in the shadows. It's just a matter of preference.
Experiment with both in a doodle to find out which you prefer.