Down the back of one's neck, mostly (3)
I believe the answer is:
nap
'down' is the definition.
(close in meaning in sense of hairy surface)
'back of one's neck mostly' is the wordplay.
'back of one's neck' becomes 'nape' (nape means the back of your neck).
'mostly' means to remove the last letter.
'nape' with its final letter taken away is 'NAP'.
'the' is the link.
(Other definitions for nap that I've seen before include "A fuzzy surface texture" , "one akin to whist" , "A brief informal sleep" , "A brief sleep, forty winks" , "A short day-sleep" .)