Mostly avoid having to do winter sport (3)
I believe the answer is:
ski
'to do winter sport' is the definition.
(skiing is a winter sport)
'mostly avoid' is the wordplay.
'mostly' means to remove the last letter (most but not all of the word).
'avoid' becomes 'skip' (skip can mean to avoid or pass over).
'skip' with its last letter taken away is 'SKI'.
'having' acts as a link.
(Other definitions for ski that I've seen before include "Winter sport attachment" , "Narrow runner built for travel in snow" , "Go downhill rapidly" , "Pole? How one often ends" , "Descend fast" .)