The most common and most likely answer to this crossword clue is the 5 letter word TAHRS
I've seen this crossword clue in The Guardian
T
A
H
R
S
More clues leading to the result TAHRS
Buddy explains!
The straight part
We know that "they’re horny" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they’re horny = tahrs.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 TAHRS mean?
TAHRS noun- Any of three genera of large Asian ungulates belonging to the subfamily Caprinae (goat-antelopes).