The most common and most likely answer to this crossword clue is the 4 letter word NESH
I've seen this crossword clue in The Times
N
E
S
H
Buddy explains!

The straight part
We know that "Feeling cold" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case feeling cold = nesh.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 NESH mean?
NESH adjective- Soft; tender; sensitive; yielding.
- Delicate; weak; poor-spirited; susceptible to cold weather, harsh conditions etc.
- Soft; friable; crumbly.
- To make soft, tender, or weak.
- To act timidly.