If you want to make a large fortune into a small fortune, take up horses. You don't make money in horses unless you're incredibly talented, incredibly dedicated, and willing to do whatever it takes to make your dream work. As training goes, you often don't make enough money to live well on, and sometimes you have to sacrifice the wellbeing of the horse to make your training profitable. If you end up training competitive riders, you'll have to constantly be learning and training yourself in order to properly teach your students. You'll need to put a lot of time and effort into the horses and riders under your tutelage. If you end up training children, you'll do the same exact exercises over and over again, you'll watch as kids bounce around on the back of your own horse (since most riding instructors who focus on children use their own horse for lessons), and you'll deal with crazy parents who either don't want to be at the barn at all, or who think their kid is going to the Olympics on horseback. I've known so many trainers who genuinely love horses, but have fallen out of love with riding and being at the barn because they make their money training. It's a great way to make yourself hate riding, unless you have the heart and dedication for it (and sometimes even that's not enough). If you get to the point where you can pick and choose the people and horses you work with, where you can train the way you believe in and think is best, then it's fabulous. But it's rare that you make enough money to live well on doing that.
As for competitions, I can almost guarantee that you'll end up spending more on the competitions, and everything that goes into competing, than you'll get out of it. It's not a legitimate way to make money unless you're competing at the upper levels (and at that point, you'll likely need a horse that was specifically bred and trained for your discipline and level of competition, which can cost tens of thousands of dollars...). Even those riders who compete at the upper levels don't always make enough to live comfortably on through that alone. To be honest, they often have money to begin with and don't have to worry about how much they make from competing.
To be honest, the fact that you quit pony club because all you did was take care of horses and barely got to ride tells me that you should absolutely not be working with horses. That's literally what working with horses is. If you're a trainer, you'll be spending most of your time working with other people and their horses. You won't be riding much. Even if you're a trainer that rides other people's horses and trains the horse, you'll more than likely be riding "problem" horses and fixing issues, which isn't the most fun and can be quite dangerous. If you're a competition rider, what do you think most of your time will be spent doing? Keeping up your horse, mucking the stall, feeding and watering the horse, etc. If you want to spend more money, you can board at a facility that does all that for you, but then again that's just one more expensive bill to pay when you likely won't be making much money to begin with. If you're a seriously competitive rider, you'll constantly be training, working hard to make it to the next level at a show. It's not all fun and games, it's serious work. You'll be at the barn constantly, riding every day to keep you and your horse in the best possible shape.
If you loved horses more than anything, you'd have been excited and happy just to be around them at pony club. When I was 6, all I wanted was to be able to be around horses. If I got to ride I was ECSTATIC, but I was also incredibly happy just to groom the horse. I mucked stalls and cleaned tack so I could afford to take lessons, and I loved every second of it simply because I was around horses. THAT's what you need to make a living working with horses, and even still I only do it part time because I want to be able to choose who I work with and how I train. I have a full time job that pays my bills, and that I enjoy, and horses are my hobby and passion that I'm lucky enough to make a little money with on the side (but honestly the money I make working with horses doesn't even cover the care and upkeep of my own horses...even if I was doing it full time with a full roster of students, I'd struggle to make ends meet).
If you love riding, that's wonderful. Take lessons, maybe even lease or buy a horse, but if you aren't willing and happy to put a lot of time, effort, sweat, and tears into it please don't try to make it your job. You'll only end up regretting it. Get a job that will pay your bills and ride for fun.