Passenger’s vacuous reaction to cold city (6)

I believe the answer is:

prague

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'cold city' is the definition.
'Prague' can be an answer for 'city' (Prague is an example). I'm not certain of the 'cold' bit.

'passenger's vacuous reaction' is the wordplay.
'vacuous' suggests removing the centre.
'reaction' becomes 'ague' (I can't justify this - if you can you should believe this answer much more).
'passenger' with its middle taken out is 'pr'.
'pr'+'ague'='PRAGUE'

'to' acts as a link.

Can you help me to learn more?

(Other definitions for prague that I've seen before include "Gear up for this European city" , "European capital" , "Capital city of Czech Republic" , "Rather quiet" , "Czech Republic's capital" .)

I've seen this clue in The Times.

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