I personally see no wrong with it as long as the person is the legal age. In NY the legal age to ride a horse without a helmet. Now I know there are some kids that are skilled enough to be able to...like mlkarel for example (just chose her because I just finished looking at pictures of her and duke).
But I have to admit that there are some girls that I know (not on here...in real life) that just horse around WAY too much in the saddle to not wear a helmet...so that's my main reason why I say kids under the legal age should wear helmets.
I've ridden without a helmet, but I trust Sonny completely and I can tell what he'll do before he does it...but I always wear my helmet if I am on another horse just because I don't know that horse as well and I'd rather not risk it.
Why did I bring this up? Well the girls that I ride with wanted to ride without helmets and said they'd just do walk/trot...no canter or jumping.....and I told the BO that I thought it was a bad idea so she said they couldn't do it. And then the girls (well mainly just the one) got all 'POed" at at me and kept doing STUPID things to prove that her horse wasn't going to do anything...and she dind't understand that horses are stil animals and CAN do things without reason or thinking.