Crossword Genius

Admit having won somehow on a horse (3,2)

Ross

I believe the answer is:

own up

I'm a little stuck... Click here to teach me more about this clue!

'admit' is the definition.
(I know that own up is a more specific form of the action concede)

'won somehow on a horse' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'won' is 'own' which is present in the answer.
The remaining letters 'up' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'having' acts as a link.

Can you help me to learn more?

(Other definitions for own up that I've seen before include "Admit to wrongdoing" , "Come clean (about wrongdoing)" , "Confess, acknowledge fault" , "Accept responsibility" , "be honest" .)

I've seen this clue in The Globe and Mail.
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