It is against the Law here in Australia not to wear a helmet on public roads, trails etc. and we can be heavily fined if riding without one. We also have to wear helmets in Pony Club, Riding Clubs, all Jumping Sports, Hacking, Children under 16 have to wear one in Western disiplines, and the EFA is now looking at helmets to be worn by all levels of dressage.
I never rode with an helmet when was younger, it was never even thought of. But with my 3 children they have always worn helmets and body vests when riding, I too have now always ridden in a helmet for the past 19 years and it has saved my life more than once.
So YES I believe that your children should wear a helmet at all times whilst riding thier horses/ponies. Your son will get used to it after awhile and it will then not be a problem..