I can speak truly from experience. While I did not buy/breed a foal and train it from the ground up (which IMO is much easier than taking a truly green three year old and starting from scratch with a horse who is 800lbs heavier than a foal and even more unpredictable)..
My Christmas present last year was a very promising green (as in she had been groomed, stood for the farrier, and lead to and from the pasture to the barn, no other formal training whatsoever) filly. I had never worked with a completely green horse before, but had about 7-8 years of experience with horses and foals on my trainers farm. I've ridden and driven her two and three year olds at various stages of their training (even a few who would be considered fairly green broke, but they all had sweet dispositions). I've watched her training and listened to her philosophy basically the whole 7-8 years she had been teaching me to ride.
Learning to understand horses isn't just about riding them or exploring them, its about observing them. Observing them with trainers, observing them on their own. They are all unique, and no matter how well you handle a horse when its a foal its still going to grow up to have a very unique personality, its true the more you handle them the better they are as they get older, but its been my experience that their personalities as foals tell nothing of the horse they grow in to be. We have a two year old at the barn who as a foal literally dragged me a few hundred yards uphill to go back to the barn, at the time my trainer thought she was going to have her hands full with her.. and she did for awhile.. but once she was weaned she was much calmer and from what I can tell she's pretty pleasurable to work with. (She's been off work for a few months due to a pasture injury... she may not be quite as mentally sound as we think hahahah)
Anyway my point is, there is no telling the type of horse your going to embark on if you get it when its six months old.. You could have a very calm and tolerable horse at that age, and once it matures and realizes its strength could be a different animal.
My filly was a little nuts from the start. I've always considered myself a good rider, my trainer was in full support of me getting this three year old and embarking on the journey.. and up until recently (almost a year later) I doubted myself almost every step of the way. She broke countless sets of cross ties, her cast iron feed tub, pulled me off my gelding when I was ponying her, bucked me off one of the first times I was riding her (it was my third time riding her), sent a hoof toward my head, reared and bucked under saddle countless times.. and in all honesty, she's relatively sane. She's definitely not a beginner horse, but in general training her was not all that difficult compared to some horses (or even colts). Again, I didn't have her first three years to work with her, and I think she would have been a lot more calm and trusting at that point.
The first maybe 6-8 months of her training had to be about building trust, which I didn't realize at first. I knew she didn't understand why I was doing these things to her, but I thought a lot of it had to do with her disposition... Her instinct, I think, was overpowering her demeanor. She's normally a very curious and sweet horse who loves to show off. She was scared and confused and quite a few times I found myself jumping from rock to rock instead taking the baby steps required to get to each rock. I didn't do anything mentally traumatizing to her, but my ignorance cut us both short of the experience a little bit. As in, we achieved certain milestones negatively when they could have been done so positively.
Now, I'm in college so I can't ride her as much as I want.. but the last few times I've ridden her she's been amazing. She hasn't lost much, if any, of her training and she's been a lot more levelheaded then her usual somewhat nuts self. I think that's because she's comfortable and understands what I want from her now and we're beginning to form a trust relationship.
One big trouble you will have, is figuring out how to react to bad behaviors. Like if they kick at you or bite you. Everyone will tell you something different. Some say don't hit them by the mouth, they'll get headshy.. Others say don't hit at all just be aggressive with your tone.. Others are in favor of physical punishment for a physical wrong. In all honesty, I believe it depends on the horse. Some horses are extremely UNsensitive (which is not a word) but could care less if they get hit, will never get headshy.. actually bite for the attention hitting gets them, etc.
Honestly, occaisionally my gelding will send a little nip my way and I give him a smack on the nose. He doesn't care, he's not head shy and the biting subsides until he gets a little ballsy again (usually days or weeks later). My filly though, is already naturally headshy. I'm sure I could give her a little smack with no change, but a "little" smack defeats the purpose... she would barely feel it and it wouldn't register as a punishment. If I really gave her the smack that would startle her enough to not bite me again, I think she would become even more headshy, so I make a big commotion with my voice and either give a little yank on the lead or hit her barrel or butt which she doesn't mind at much.. but it still registers as "oh I better not do that again.."
Anyway my point is, there is a lot more to it than it looks. You have to have a LOT of patience. They will do things with no intention of being bad and you get faced with a lot of predicaments... You find yourself taking more steps backwards than forwards a lot of times. If you do it, you have to be able to commit fully, especially with a foal. Foals get feral quickly! They need daily handling, touching, rubbing, grooming, hoof picking, etc. A good breeder will have weaned a foal that already grooms, will stand for a farrier, even clip with clippers and have basic ground manners down.
The first day I had my mare, I lunged her a little bit (which she never did before, and was surprisingly fine with.. [you'd be surprised how some horses don't get the running-in-a-circle-around-you] she picked up the voice commands quite quickly and I didn't even need a whip (holding up a whip sent her into the fastest semi-gallop she could muster on such a small circle.. no matter how many times I showed her the whip or rubbed her with it, or let her smell it.. now she doesn't mind it as much but if I lash it, she goes!).. anyway I lunged her for a few minutes each way.. then let her loose in the arena and just observed her. She showed off for a long time before I finally caught her. Trotted fancily, galloped, etc. I still have pictures from that day I took of her.
I'm getting lengthy haha, or I was like 6 paragraphs back. Anyway I think the decision is yours. Before you embark I would suggest getting as much as experience as you can. Ride every type of horse you can, make sure you can ride a buck, a rear (I'm not saying instigate a buck or anything), you can stop a horse trying to gallop away with you (especially if you have trails), your confident in lunging and long-lining (many people don't long-line before they ride, but I wouldn't ride a horse who wasn't at least a decent long-liner.. they learn to hold the bit in their mouth, themselves, basic stopping and turning, three speeds at the trot, voice commands, trust, turning on a rein, etc.)...
I highly suggest taking long-lining lessons!! I never really did it before I got my mare, but I took a few lessons then I did it with my gelding until I got comfortable.. Long-lining probably saved me from getting bucked off several times... just because she was used to the bit and carrying it in her mouth, she was sound with all kinds of weird equipment on her, she didn't mind side reins or a martingale (I longlined her with a martingale before I rode her with one) you can test a lot of equipment in a bitting harness.. you can tell their personalities, you can teach them the idea of the rail and turning. You can put them in a bitting harness as late yearlings, and by the time you saddle them they can have a good year give or take of steering, stopping, turning, circling, going in straight lines, etc. which you have no idea how much it helps unless your deprived of it. (I had about two-three good months and it still helped a lot, but we would make random turns for no reason or confusion about stopping)
Anyway I keep diverting.
My opinion is if its what you want, go for it! Make sure you're ready mentally, physically, emotionally and experience wise for it. You have to have a lot of patience, you have to have the backing of a good trainer. (My trainer gave me a lot of advice and guidance and I had a lesson with her at least once a week.. up to three times a week with my mare.. which helped tremendously) Your going to doubt yourself, so be prepared. :P Honestly coming here for advice is sometimes worst than listening to your gut, just because everyone has a different style and a different way of approaching it. It does help as a last resort, but I would listen to your trainer first and foremost.
Good luck! :)