There's a good way to introduce your kids to horses and then there's the above way... which leads to a trip to the ER and a child that never wants to "go pet the horsey" ever again.

I work with disabled children twice a week. And even with the BOMB froof horses that we use the kid's aren't allowed to handle them my themselves. I let them walk on my right side, while the horse is on my left side, then I give them the excess lead rope to hold. The kids feel great and I have full control of the horses.

With kids that young *points above* maybe keep in in your arms away from the horses' feet and keep it as your only responsibility (as in... don't lead or handle the horses while you're carrying your offspring in your arms)