Inn, oddly chilly, back open to all (6)
I believe the answer is:
public
'open to all' is the definition.
(I've seen this before)
'inn oddly chilly back' is the wordplay.
'inn' becomes 'pub' (I've seen this before).
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
'back' says the letters should be written backwards.
The alternate letters of 'chilly' are 'cil'.
'cil' in reverse letter order is 'lic'.
'pub'+'lic'='PUBLIC'
(Other definitions for public that I've seen before include "Serving the people" , "Accessible to all" , "School or house" , "Community in the open?" , "Overt" .)