The most common and most likely answer to this crossword clue is the 10 letter word CHINCHILLA
I've seen this crossword clue in Financial Times
C
H
I
N
C
H
I
L
L
A
More clues leading to the result CHINCHILLA
- Relax wearing friend's fur
- Furry creature to relax in the country
- Relax in country that's warmer?
- Cold friend's wrapped in warm material
- Fur seen in country with cool interior …
- Relax wearing mate's fur
- Fur that keeps part of the face cool, did you say?
- Animal has a sudden feeling of fear in the country
- Rodent getting cold in country
- Face bit cold? Answer’s fur
Buddy explains!

The straight part
We know that "Animal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case animal = chinchilla.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CHINCHILLA mean?
CHINCHILLA noun- Either of two small, crepuscular rodents of the genus Chinchilla, native to the Andes, prized for their very soft fur and often kept as pets.
- The fur of a chinchilla, used for clothing.
- A variety of Persian cat with white fur and green eyes.