Generally, this term is used by those who need to release urine. The symbolism of "long horse" and "short walk" are up to the user's interpretation.
John: You know, though our conversation is enthralling, I admit I must taking the long horse for a short walk. In other words, I must urinate, as you may know from the saying's entry on Urban Dictionary.
Jane: Ok.
Joseph: It’s November 16th, you know what that means
Albert: Go fuck yourself
Throw a Short Person Day gives you 5 free throw someone under 5’4” passes