According to Albert Munsell, who was a painter and art teacher and inventor of the Munsell system of colour, colours do not have just one property, but instead is comprised of the value (lightness or darkness of the colour), chroma (intensity – brightness to dullness of the colour) and hue (the colour) and undertone (relative warmth and coolness of the colour).
Here we have a Monet that is light in value
Here we have a Monet that is mostly deep in value.
Here is a mostly bright and clear (high intensity) picture
and here is one that is muted and has a low saturation of colour.
This picture has a warm undertone
This one has a cool undertone.
So green (or any color) can be warm or cool, light or dark, bright or muted, all at the same time! So of course you can have a light cool green, or a light warm green, that light cool green could be brighter, or more muted, it could be really light or only medium light. It could be a very cool green or only a slightly cool green.
When we think about these different aspects of color and colors that blend well together, we may look for overall light, cool and clear colors, or alternatively warm, deep and muted colors (as a couple of examples).
It would look very odd if Monet had put a bright color or two into a muted painting, just like it doesn’t work in interior design or when combining colors in clothes if we combine colors that have no properties in common together.