Below is purely my personal viewpoint.....
For the painter....grey is far from simply mixing 'black and white'.....which white....which black....there are several of each!
Simply adding a red for 'warmth'....or blue for coldness is another minefield of....which red and which blue out of the many available to the painter.
Grey is very far from any other colour in it's complexity....and...has so many possibilities beyond what other colours have for subtlety.
Over the years....I have adopted an easy approach to using a standard (out of the tube) colour for the so called 'warm and cold' approach.
I use Old Holland Warm Grey Light and Old Holland Cold Grey....as they are as good a starting point as any....and can quickly be adjusted with the addition of other pigments....depending on my need
There is no limit to what other colours can be added to a 'base' grey mix....it all depends on what you are trying to replicate.
When it comes to shading and high lighting....in very general terms....and for the best effect...avoid using pure black or white....unless you want very strong contrast....which is rarely the case with grey's.
Jason has given a good example of just how many variations there were of Confederate 'Grey'.....none of which could be reached with a simple mix of black/white and red or blue....but rather....ochre's/browns and green's.
Of course....if you already know all this Gino....please ignore my rambling.
Regards
Ron