Starting off with one tiny point- I LOATHE the term "Break" I would like to remove it from the equine vocabulary.
I have saddle trained hundreds of horses, I have harness trained quite a few BUT I have only ever "broken" one, and he very badly needed it, and was doing his very best to break me into very small pieces!!!!
So, forget "breaking in" and think "train"
Look at your sweet little boy- how hard do you think it is going to be, once he is fully grown (no less than a full three years old) and gelded, to persuade him to let little kids sit on his back??
Yes, you are right, not hard at all.
There are lots of things you can do to help. You can get him used to a surcingle- the strap that goes right round his belly- in my experience it is this tightening that causes almost all and any reaction you are likely to get from a young horse. You can do that now, he is quite old enough. Just get a belt, or buy a proper surcingle from Ozark Tack, if you would rather, and start putting it on him when you walk him out. You may get a few fireworks the first time you do it up tight, you may not, depends on the horse.
Since your children are really young I would suggest you do no use a bit, but yo will want to drive him later, so teaching him to wear a bit will be useful- again, by Spring he will be old enough to start this- you will need help fitting it properly and getting the right size- the first few fittings should not be done by a Novice- and NEVER let your kids hold anything attached to the bit, even as a game, as real damage can be done. By the time he is three years old he will just extend the game to carrying the kids- most Minis are really generous about this sort of thing, although I have to say, I backed and trained all my Arabs the exact same way and I never had any trouble with any of them.
Quiet and slow and steady gets the best trained, quietest horses.
How big is your boy likely to get, any idea??
When you work out how mush weight he can carry, remember to take the weight of the saddle into account- this is the main reason most Minis are cart trained- they can pull a lot more than they can carry.
It's lots of fun, too!!