After thinking more, I had a little more input for you. There are some points I'd like to bring up.
First and foremost, the horse world is a very physical one. Any position you get that requires you being active would be heavily impacted if you're involved in an accident that disables you, even for a temporary length of time. Whether you're hurt or not, life goes on and horses need care. If you're out of the game, someone's going to need to fill in your shoes. It's a lot like if you were planning on figure skating (or any sport) as a source of income. If something happens, you need a fall-back plan that can still provide for yourself and your family - one that you can practically do if you've been hurt. It doesn't necessarily have to be a tragic loss of limb or paralyzation, either. Something as simple as injuring your knee or back and needing surgery or time off will impact the job. And this is where you have to be practical and level-headed. If it's a choice of your back and ability to walk or riding a horse, you need to choose your health first. It sucks. I speak from real experience. But to keep riding and further damage yourself is beyond silly and very unrealistic. I'm in no way saying you would do this - but instead giving you an example of what could happen.
Secondly, even though it is never too late to start a journey in horses and riding, there ARE people out there who have been involved longer than you. If you want to become a... Trainer, for example, and focus on trouble horses, you'll be in direct competition with people who have been at it longer and have more hours and time in the saddle. Most folks will want someone more seasoned. Same for lesson instructors, chiropractors, vets and so on. You're going to want to accumulate saddle and riding time, as well as horse experience, over several years, both for your knowledge and your 'resume' so to speak.
In regards to a "formal education" and being careful, I know a person who went to the CSU equine program, a really fancy school in Colorado. Prior to schooling there, she had established a decent training-client base and provided frequent lessons to a pretty reliable group of kids. She had been in the saddle since she was six, trained sane and rational horses and worked well with almost all learning styles. She got the bachelors degree, hoping to one day start her own training/lesson barn.
Then she hurt her back. She couldn't keep up with the green horses, so she lost a lot of clients.
Then she got pregnant, lessons fell by the wayside as she suddenly needed a more stable and secure job. Luckily she had gotten a Masters in business, was able to land herself a less physical job with enough salary to own two of her own horses with no need to sell lessons or training to help support them. She is now expecting her second kid, and is mich happier, even though she's still paying the student loans for the equine education and went really far into debt, only to still have a "boring/desk" job.
With these things being said, I'd really suggest pursuing horses and competing them as a hobby first while setting yourself up for a financially successful future in other ways. Being in and around the industry will help you put your feelers out there and get a solid idea of what you are actually and realistically interested in. You might, after a few months, decide you actually hate showing. Or maybe you're interested in Western riding after all. The fact is, with as new as you are to it, there's a whole lot you don't really know and that's ok! Take this time to learn and build muscle, enjoy yourself and have fun!