12 year olds ovulate and have cycles. Post-menopausal folks don't ovulate, yet can still be horny and still orgasm. So do folks that have had surgery to remove their ovaries. And so do folks that ovulate irregularly. Many women who ovulate regularly aren't all that horny (I've met them, and I'm happily not one of them) and some women go large chunks of their life, having children and jobs and everything, but rarely orgasm. Other women aren't realistically pain-free or worry-free enough without birth control to manage to be horny and/or orgasm. Needless to say: Ovulating doesn't mean more horny and more likely to orgasm.
Hormones/ovulation are only part of the story.