Crossword Genius

A criminal wearing many clothes heading for arctic air (4,2,1,6)

Ross

I believe the answer is:

away in a manger

I'm a little stuck... Click here to teach me more about this clue!

'clothes heading for arctic air' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'a criminal wearing many' is the wordplay.
I cannot really understand how this works, but
'a' could be 'an' and 'an' is located in the answer.
'wearing' could be 'in' (in jeans or in a dress) and 'in' is present in the answer.
'many' could be 'm' (Roman numeral for a thousand) and 'm' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for away in a manger that I've seen before include "Familiar tune" , "song?" , "Christmas carol" .)

I've seen this clue in The Times and The Sunday Times.
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