What does 'cold' mean? What does 'warm' mean?

"Warm is used by a salesman to encourage you to buy their product.

"Cold" is used to criticize a product. A salesman may use this to discourage you from this item.

Another descriptor with a positive connotation that I like is "meat on the bones".

If you're dealing with a system, or a sound, in which no agreeable balance can seemingly be struck between warm and cool, i.e. a sound that can be made to be either too cool or too warm, but offers little or no real appreciable apparent, or satisfying, 'sweet zone' in the middle, then you have a sound that is said to have little or no "inner warmth". 

A system or sound with a good deal of inner warmth will, by definition, sound neutral without also sounding threadbare. As opposed to an overtly warm sound that may be described as 'pleasing', but strictly speaking is neither accurate nor neutral.

Universally accepted as terms, but for me neither is correct when it comes to balance or neutrality.
G

We are all in agreement (except for Fred, he never agrees with anything) we just may not always know how to get to the good sound we're looking for.

Surprised no one yet has invoked the presence of different harmonics, at different percentages in different ratios.  As @newbee says, it's at least partly a product of variations at certain points in the frequency range, but the relative presence/absence of harmonics is part of it too.