Look at American soldier with cold reason (5)
I believe the answer is:
logic
'reason' is the definition.
(logic is using reason)
'look at american soldier with cold' is the wordplay.
'look' becomes 'lo' (archaic exclamation meaning 'look!').
'at' means one lot of letters go next to another.
'american soldier' becomes 'GI' (informal term for a US soldier).
'with' says to put letters next to each other.
'cold' becomes 'c' (eg on taps).
'lo'+'gi'+'c'='LOGIC'
(Other definitions for logic that I've seen before include "Reasonable judgement" , "Rational thinking" , "Dialectics" , "Sound sense" , "Reasoned thinking" .)