This is a term for the clitoris. This term came to fruition in a small South West Kansas town called Meade in the year 1995. While exploring Kama Sutra like moves, the 69 Handstand, a cowboy noticed that the cowgirl's vagina had a remarkable similarity to a horse saddle. Oddly enough the clitoris was in the right location in comparison to a saddle horn. Thus the term Gini Horn was concieved.
Abner: Hey Paul, what cha doin tonight?
Paul: Well...I think I'm gonna saddle up on muh old lady and tickle her Gini Horn for a spell.
Abner: Well don't get a charlie horse on your tongue!