We usually hear "He is a cool guy" when referring to some hippie or a funky person. However the tone changes dramatically when cool becomes cold. We say "Her behaviour was cold" to mean someone who is unfriendly.
What is the exact difference between the words in different contexts, say, temperature, demeanour, etc? Why have they developed a semantic difference despite their similarity?
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.
Cold means, "without emotion; unfriendly"; cool means, "not friendly, interested or enthusiastic."
The difference is that cold generally means that somebody is less friendly than somebody who is cool.
Cool is also informally used to show approval or admiration; that is what happens in the following sentences:
You look pretty cool with that new haircut.
It's a cool movie.
Similar meaning is given to cool in the following sentence.
A: We're meeting Jake for lunch and we can go on the yacht in the afternoon.
B: Cool!
I am bit surprised that all the previous answers to Sultan focus on the meaning of "cool" and "cold" as first of all referring to the personality of people.
To me, as a non native speaker, "cool" and "cold" are first of all something denoting temperature. Just like "hot" (which can, similarly, also refer to personality or look).
Like a in "cool breeze", or a "cold winter".
In this case "cool" and "fresh" as closer. Cold is something more "extreme" (say, closer to 0 °C), like ice (frozen water) or close to that. ;-)
