IMHO teaching them to drive at 7 (if you have a "cart for two") would be so much easier than teaching them to ride at that age. If you can sit next to them, let them put their hands over yours at first to see how it "feels". Then (yes, in an enclosed area) let them try to direct the horse while you explain and direct. You can always reach over and take the reins or you could hold on to the bottom of the reins that are dangling below their hands (just in case). At any rate, a VERY reliable horse is needed so the child's experience is a positive one.
My granddaughter wants to be around the horses like her Gamma but she is here so little that she lacks confidence. She always asks to "ride" (leadline) but, as you know, it takes balance which at 5 she doesn't have total control yet. So we tried the cart and when she found that she could get the horse to turn and stop etc. from a "safe" spot in a bench-like seat, she was thrilled.
The biggest thing to remember is it must be the child's idea. Just like you "can lead a horse to water but can't make him drink". You can WISH a child to share your enthusiasum about horses but you can't MAKE them "horse happy". [hard lesson for me]