One church that is very cold (3)

I believe the answer is:

ice

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'very cold' is the definition.
'ice' can be an answer for 'cold' (I've seen this before). I am not sure about the 'very' bit.

'one church' is the wordplay.
'one' becomes 'i' (Roman numeral).
'church' becomes 'ce' (abbreviation for Church of England).
'i'+'ce'='ICE'

'that is' is the link.

Can you help me to learn more?

(Other definitions for ice that I've seen before include "Glaciate" , "Decorate with frosting" , "Diamonds (slang)" , "If it's thin, skating on it can be dangerous" , "It's cold and slippy" .)

I've seen this clue in The Guardian.

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