The most common and most likely answer to this crossword clue is the 4 letter word SCAG
I've seen this crossword clue in The Times
S
C
A
G
Buddy explains!

The straight part
We know that "Horse" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case horse = scag.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 SCAG mean?
SCAG noun- Heroin.
- (originally African American Vernacular English) A woman of loose morals.
- A cigarette.
- To destroy the data on a disk, either by corrupting the filesystem or by causing media damage.