Adjectives – Understanding Temperature Descriptions: Hot, Warm, Cool, and Cold

Originally, cool meant someone who was somewhat standoffish in their demeanour, or someone who does not get too involved - and cold was just a more extreme form of that.

As Bill Franke points out, the meaning of cool meaning popular or trendy probably originated with cool jazz in 1945 and began being used to describe people in the 1950s seeing a rise in usage through the 1960s and a large spike in popular usage in the 1980s and 90s:

For this reason, "he's a cool guy" in modern English means "He is a trendy (or fashionable) person" rather than "His character is standoffish", whereas the meaning for cold never evolved to mean trendy, and retains its older meaning of someone who is very detached and unemotional.

If you want to use cool in the sense of someone who is slightly unemotional, you might prefer to use the idiom He's a cool cat or He's a cool character which both retain the old (non-trendy) meaning of the word cool. Alternatively you can say something like His response was somewhat cold as a less ambiguous alternative to His response was cool.

The easiest way for a native speaker to distinguish between a descriptive and classifier adjective is to attempt to intensify it. Consider the following:

• The old train
• The very old train
• The steam train
• *The very steam train

While you can intensify descriptive adjectives (the very old train), you can't do it to classifiers, at least without some kind of strangeness.

Another test that can be applied is paraphrasing the noun phrase as a sentence that uses the verb be. In the example above, you can say the train is old, but not the train is steam.

You can also try to fit in another classifier before the one you're trying to test:

• The old teacher
• *The math old teacher

English doesn't allow for this type of structure if the adjective is descriptive. However, this is a one-way test only - you can't test whether something is a classifier because you can have a classifier followed by another:

• The revolving doors.
• The automatic revolving doors.

Of course, this is less straightforward for a non-native speaker, who won't necessarily have that intuition that tells you whether a phrase is grammatical or not.

Some combination of the above is probably going to work for you, with the easiest being the intensifier.

For your specific example, let's apply some tests:

• "an old political idea"
  the political idea is old - descriptive

• "latest educational reform"
  The latest reform is educational - descriptive

• "leather dancing shoes"
  The dancing shoes are leather - descriptive

You can find out more by searching for epithet vs classifier tests, which produced some of the tests I've noted above.