The definition of horny ... is simply another word for being hungry for love. "I am horny for you" means precisely "I am hungry for your love" - vs hungry for love in general. "I am horny for you" thus means I am ready to be loved BY you and I am ready to GIVE love to you - i.e. to make love with YOU.
James Joyce even used the term in his Ulysses.
This word was first recorded in 1889.