Saint Nick has no time to wrap posh sweater (5)

I believe the answer is:
sauna
'sweater' is the definition.
(saunas make people sweat)
'saint nick has no time to wrap posh' is the wordplay.
'saint nick' becomes 'santa' (I've seen this in another clue).
'has no' suggests deleting specific letters.
'time' becomes 't' (abbreviation).
'to wrap' indicates putting letters inside.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'santa' with 't' removed is 'sana'.
'sana' going around 'u' is 'SAUNA'.
(Other definitions for sauna that I've seen before include "Scandinavian hot room for cleansing oneself" , "Sweat room" , "Form of steam bath" , "Steam-bath" , "Finnish steam bath" .)