DON'T DO IT.
You'll regret it. Trust me, I've been there. I know it seems like a good idea to a lot of parents to have their kid "grow up with" their horse, but it doesn't work like that in the real world.
It's cute for about two weeks and then the novelty wears off and you're left with a really big problem. Why? Because baby horses are naughty, uneducated little accidents waiting to happen if you don't know how to train them. They're a massive investment of time and money and should only be taken on by experienced horsemen. They are NOT safe for children. And it isn't fun anymore after your kid gets kicked or run over by a belligerent colt. Foals are frisky, mischievous little buggers. They like to roughhouse. They don't understand that children are delicate and that they have to be on their best behavior around them. Even though foals are small and cute, they are still strong and dangerous. And it gets worse when they're one and two years old. It's like trying to control an 800 pound teenager with an attention span of three seconds!
Furthermore, your kid is not going to want to wait three years to be able to ride their horse. Actually, scratch that. No greenbroke three year old is kid safe. You'd have to put a lot of miles on the horse before you even think of putting kids on it.
Can you afford a trainer for all those years to teach the thing to load, tie, bathe, clip, lift his feet, pony, and all that good stuff you should teach a horse before you ever put a saddle on him? Then you need the trainer to break the horse and get him trained enough for beginner riders, and who knows how long that would take. At this point, your kids are probably getting impatient and losing interest.
My parents bought me an unbroke 2 year old for my first horse, with the intention of us "growing up together". Of course, I didn't know any better either, and it soon turned out to be a huge mess. The horse was sedated when we went to look at him and when we brought him home, he was a nightmare. He was pushy, rude, obnoxious, and dangerous. I sure as hell couldn't handle him. The only thing I could do was sit in his stall and brush him. He eventually turned out to be a wonderful horse with several years of maturing, a couple of good trainers, an emotional roller coaster ride, and a huge chunk out of my mother's wallet (can you guess who it was? It was Norman!). Would I go through that fiasco all over again? Probably not, and I would advise anyone else to make a wise, clearheaded decision when purchasing a horse. ESPECIALLY if you're getting one for your children. Go for a good 'ole, middle-aged, dead broke, babysitter-type horse. It doesn't have to look like a perfect little show pony, either. ALL horses are beautiful to kids, and they're just happy to have one.
Raising a foal can be a wonderful and extremely rewarding experience, IF you know what you're doing. But don't even think about it if you're a non-horsey mom or dad who wants to get your kiddie a horse. Mkay? Don't.