Crossword Genius

State and territory have cooler city with American Christmas visitor (5,5)

Ross

I believe the answer is:

santa claus

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

'christmas visitor' is the definition.
(I've seen this before)

'state and territory have cooler city with american' is the wordplay.
I cannot quite understand how this works, but
'state' could be 'us' (U.S. is an example) and 'us' is present in the answer.
'and' could be 'n' (common abbreviation for 'and') and 'n' is located in the answer.
'city' could be 'la' (Los Angeles) and 'la' is present in the answer.
'american' could be 'a' (common abbreviation - e.g. in organisation names) and 'a' is found within the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for santa claus that I've seen before include "Seasonal visitor" , "stocking filler - with 6 dn" , "a winner with children?" , "A Derby winner" , "St. Nicholas" .)

I've seen this clue in the Sydney Morning Herald.
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