Short answer: as far as you want to go, assuming you have the time, money, and ambition to do so. You do not “age out” of horse sport as you could/would for going pro/competing in the highest levels in almost any other sport.
Long answer:
The three limiting factors to your success are going to be time, money, and ambition. I’d dare say that ambition is the biggest limiting factor of the three; with the right amount of ambition, one will tend to find the time and money to make their goals happen. Without ambition, it is much easier to let things slide by the wayside.
Money: unfortunately for us equestrians, our sport is extremely expensive. Unless you happen to own land, you have to board your horse somewhere and regardless, you have to pay for coaching. I can only give examples of my own experiences. Of course you have to pay for board, lessons, farrier, vet, incidentals etc, I just did the math and my basic costs run about $20k/year, for reference I board at a nice facility with an accredited coach, and only lesson 2x/week. Shows vary wildly, but even a local multi-day show here runs $750-$1500. To hit up the bigger circuits are in the solid 4-figures to 5 figures per show.
Pros typically don’t show their own horses, they campaign horses for owners; the issue here is that many pros were practically born in the saddle and had successful junior careers. You have a bit of a disadvantage here that you’d have to prove yourself by yourself or find someone willing to take a chance on you, but you may have to foot the bill a lot more.
Time: I’m an adult amateur that competes only in the local circuit, I only attend a handful of shows per year. I only have one horse, and ride 5 days/week, I figure that on average I dedicate about 25 hours per week to my riding habit, between travel, prep, riding, caring, etc. I have to use a lot of vacation time to go to shows, which means less time with my SO, and significantly less money for vacations.
It can get tiresome, and I’ve burned out a couple of times already in my 25 years of being in the sport and had to take some time away from being in a competitive program.
When in a competitive program while working full time and trying to keep up with running a house, there isn’t a whole lot of time for other things.
Can it be done? Absolutely. You’ll have to be willing to sacrifice a lot to get there, but it is most certainly doable.
Oh, I forgot one more thing: Injuries
As you age, you don’t “bounce” as well; you can get injured more easily and more seriously, recovery can take a long time. I had a bad fall (freak accident, not a naughty move on the horse’s part at all) a few months ago and ruined my dominant shoulder. My shoulder will never be the same. I was off work completely for 2.5 months, and am still on part time days. I have been sidelined, and am currently not riding. It’s killing me to be out of the saddle so I may try to get back on to hack soon, but I won’t be back to any semblance of where I was for many many more months.
Thank God I have good insurance which allowed me to take the time I needed to recover before having to return to work.
Moral of the story: Injuries can and do happen, have good insurance and a contingency plan.