Went on horse to ring at cowboy show (5)
I believe the answer is:
rodeo
'cowboy show' is the definition.
(I've seen this before)
'went on' is the wordplay.
'went' becomes 'rode' (I can't justify this - if you can you should give a lot more credence to this answer).
'on' becomes 'o' (I've seen this in other clues).
'rode'+'o'='RODEO'
'horse to ring at' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for rodeo that I've seen before include "cowboy carnival" , "A bunch of cowboys, showing" , "Western show" , "Wild West contest" , "Exhibition of cowboy skills" .)