Thank you for your answer floAr I'm be up-voting your answer for giving me the term I was searching for:
Ambient lighting - lighting which is from no particular source but which is background lighting across all entities.
I've found this blog post with some very simple code which I'll be trying later.
this is the key for me:
new Color(ambientColor.R / 255f * ambient, ambientColor.G / 255f * ambient, ambientColor.B / 255f * ambient);
From the blog post:
(the approach is to modify the color of every sprite when drawing it)
Add to the top of your game class:
float ambient = 1f;
Color ambientColor = Color.White;
In the Update method:
KeyboardState c = Keyboard.GetState();
ambient -= 0.01f;
if (ambient <= 0)
ambient = 1f;
And finally, to apply ambient lighting to sprites:
Color drawColor = new Color(ambientColor.R / 255f * ambient, ambientColor.G / 255f * ambient, ambientColor.B / 255f * ambient);
spriteBatch.Draw(mySprite, new Vector2(0,0), drawColor);
As you see, it's very easy :) With this, you could simulate for example day cycle.