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.