I think it's possible to get a young horse that is suitable for a beginner, but I don't see why anybody would do it.
It's a bit of a game of risk, horse buying.
To me, a good horse is composed of four factors, temperament, physical suitability, training and experience. When you lack any of those things you're looking at a horse who, at the very least, needs work. To me, a beginners horse is a horse that can teach the rider and help the rider where as a horse that needs work cannot do those things. Even your best three year old is going to be lacking in training and experience purely because of physical time restraints. There is no way past that fact. Adding to it a three year old will learn any bad habit you have, and you need to be teaching them good ones.
So when you find an older horse, you can try him out, push his buttons, see what he has done, get trainers to find out his more advanced skills. Each one of these tests decreases the amount of risk when buying a horse. And any horse you buy is a risk, it's hard to find safe, beginner friendly mounts. With a young horse, the risk goes right up because you're not just looking for an average safe mount, you're looking for an extraordinary mount who acts like an older horse would with minimal experience and training. The risk goes way up (to me).
To top of, I don't think there is any reason why a beginner would want to buy a three year old. Personally, I think there is very little going for this age bracket of horse - in fact it's probably my least favourite. They're generally frisky, unbalanced and tiresome - kind of like the teenagers of the horse world.
It's up to you to choose, any horse you love will be beautiful, and beauty doesn't guarantee a good horse. But that's just my two cents.
Just to add - in my experience those extraordinary horses, like dead quiet young ones, they're not advertised on online classifieds much, they sell through word of mouth quickly, or their owners just don't part with them.
Bravo!!! Very well said and pretty much covers it!
Walkingmedley....I did think you were younger....glad that you are not. I got into horses in my late 30's, by complete accident, when my daughters were taking lessons and leasing a horse. Ended up being given one of those 'free' horses. She was soooooooo pretty, how could I not? She was older too at 16 years old = experienced! Oh boy. She was also not broke, which I found out after the fact and crazy. It ended up working out and she became MY horse. However, it took a lot of dedication and time. I had to be out there every single day working with her FOR MONTHS and just on the ground. Six months later, I rode her and we learned together. However, green and green is not a good combo usually. I have seen my share of horrors.
So, if you want a cute little horse that you can't love on and kissy smoochy because you are training them as a young horse and you can't ride for quite some time, and you have to be on constant guard with, and you have to dedicate lots and lots of time to consistently, then accept the challenge. You may get lucky, but you may not. If you teach a young horse bad habits, it can quickly spiral down hill and become VERY dangerous. If you become lucky and do what you are supposed to, it can be a very rewarding thing. You just have to be very realistic on what you can do and offer.
If you want a horse that you can love on, do the kissy poopoo thing, ride, show off, learn confidence within yourself in handling and riding.....then get a 'did there, done that' older horse. There won't be the months of waiting and just doing the training and maybe finding you really don't like the training, get bored with it, get frustrated and sell an unruley horse with bad habits for less than you paid to get her.