Why wouldn't you just volunteer in one of the rescues or riding barns in area? In the rescue close to me you can "foster" a horse meaning you pay comparably small fee/month and horse is "yours" in terms of care and riding. This way you'll understand what "caring for the horse" means - it's not just riding, but lots of other things involved. And it'll help you understand if horse is something you indeed want or not.
Horses are LOTS of work (especially if you keep them home). Unfortunately too many new owners (including myself, BTW ) don't realize that until they get a horse, and all the sudden almost all free fun time is gone - you have to clean, ride, pick the poop, clean the stall, you name it. It's pretty different from taking lesson in barn once/week, when you just ride and give treats to the horse (well, in some you also have to brush/saddle).
I agree - and leasing would be another good option. I understand the being on the fence and unsure if this is your own passion or pressure from your family, and I respect you wanting to determine which it really is before plunging into horse-ownership and finding out the hard way.
Don't be in a rush to label yourself, because in the end you will find labels don't matter. Be what makes you comfortable, and happy. If that includes horses, so be it, if it doesn't, so be it. Just don't let someone else make those decisions for you.