^^ I agree. Well broke, kid safe horses are on the top end of the market right now, as far as demand goes. You aren't likely to find one free. I paid 750 in this market for my pony mare, and she's worth much more in a good market, due to what a good beginner horse she is. Good, safe, kid horses are worth more than their weight in gold - and it's not the place you want to scrimp - when kids are involved.
Even with the low market value around here we pay over $1000 for a well broke animal that can do barrels. The only ones for free are the green broke that will unload you at a moments notice or the 20+ year olds that would break down if you tried to do barrels.
But you never know. Have you tried doing an ad on Craigs List?
Be careful with rescues, if you are looking for a child's mount. Rescue is a great, great thing and there are some very good horses that desperately need help - but rescue horses are often in rescue for a reason, and require more experienced riders. They are also rarely "free" - most rescues need to pay for their facility to run with adoption fees.
If you really are determined to get a "free" horse, your best bet is to put out the word to local feed stores, vet clinics, farriers etc and just be patient. I have three horses coming in to me this week from a gentleman who can no longer care for them. I wont likely keep them, but give them some training and feeding and find them suitable homes. The current owner was sent to me by my farrier, who goes to the same church as this man.