Unpleasant character wished to go by horse (3,3)
I believe the answer is:
bad egg
'unpleasant character' is the definition.
(a bad egg is an unpleasant person)
'wished to go by horse' is the wordplay.
'wished' becomes 'bade' (I've seen this in another clue).
'to go by' means one lot of letters go next to another.
'horse' becomes 'gg' (geegee or GG is a childish term for a horse).
'bade'+'gg'='BAD EGG'
(Other definitions for bad egg that I've seen before include "Worthless individual" , "A rotten ovoid" , "Dastardly chap" , "Untrustworthy (a potential stinker?)" , "Old-fashioned no-good" .)