Find writer very cold though they entertain everyone using stylish language (10)

'using stylish language' is the definition.
I can't judge whether this definition defines the answer.

'find writer very cold though they entertain everyone' is the wordplay.
I cannot quite see how this works, but
'writer' could be 'poet' (poet is a kind of writer) and 'poet' is found in the answer.
'cold' could be 'c' (eg on taps) and 'c' is present in the answer.
'everyone' could be 'all' (all people) and 'all' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?