The saying, "we were so focused on whether we could that we neglected the question whether we should" applies here. Yes, it is possible; many people do it, actually. However, just because it can be done, it doesn't mean it should.
Where are you? I think you are looking in the wrong direction if they won't take a 33-year-old, 5 foot 6 inch (1.6 meters) person who weighs between 185 - 200 pounds (84-91 kilograms). That is not too old, too tall, nor too heavy. There is so much more to horses than just riding; horsemanship is also a very good skill to learn. There shouldn't really be an age, height, or weight restriction for learning about how to care for and understand horses.
I admire and encourage your enthusiasm, but handling horses can be a dangerous endeavor, especially if you don't know what you are doing. Horses are (usually) a reflection of how they are treated. Even if you get a perfectly "dead-broke" horse, horse's don't magically stay dead-broke. You need to find a trainer. Horses are wonderful, beautiful, and generally forgiving animals, but it is unfair to simply do a hit-and-miss messing around and rely them to compensate for all your mistakes.
I think it would be a better option to lease (not a lease to buy) a horse and get a trainer if you cannot find a program. That way, you can adjust the level of "ownership" - you won't be so overwhelmed. You can start of by a quarter or half lease. Once you get used to that, you can try a full lease before buying your own horse. Horses are (or should be) a long term commitment. That's another why lessons are a good idea. If you change your mind, you aren't shoveling money out the wazoo. Most of price of a good beginner horse come from training. Again, I won't know where you are, but here, well-trained horses go into the thousands. The cost of the initial buy, plus the care (food, possible boarding, vet bills, farrier bills, etc...), plus paying a trainer is absolute $$$$ for something you may change your mind on.
If you are so very set on buying a horse, the only option I recommend (which I don't really recommend) is to but an older, very well trained horse and get a trainer to help both of you as soon as possible.
"I hear and I forget. I see and I remember. I do and I understand." - Confucius
Last edited by LoonWatcher; 05-24-2019 at 05:44 PM.
Reason: Grammar. Rewording. Adding.