Swimmer in fur coat, much warmer, losing head! (5)
I believe the answer is:
otter
'swimmer' is the definition.
(animal which swims)
'warmer losing head' is the wordplay.
'warmer' becomes 'hotter' ('hot' can be a synonym of 'warm').
'losing head' means to remove the first letter.
'hotter' with its first letter removed is 'OTTER'.
'in fur coat much' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for otter that I've seen before include "River-dwelling mammal" , "Freshwater mammal with dark brown fur" , "River creature" , "furry creature" , "Fish-eater of the weasel family" .)