Well, I did say "barely", Bertrand. 
Certainly the absence of riding hats, and the absence of seat belts, are clues that some senior royals are just going to carry on doing things the way they've always done them. I know it isn't illegal to not use seat belts on private grounds, but modern cars have to have the seat-belt warning specifically disabled. So it's a deliberate modification.
The no-helmet thing is inexcusable. Even just falling from an ambling pony could have dire consequences, especially for an older person.
I've watched enough of those air ambulance documentaries to see how riders', cyclists' and motorcyclists' helmets have saved people from possible devastating injuries.
As for the royal train, I don't understand why that hasn't been put out to pasture, so to speak. There must be several train enthusiasts charities that would take it on and cherish it. It would not be impossible for an extra coach to be attached to a scheduled service for the occasional use by the royals. In fact, I can't imagine why the royal train needs to be used at all - short journeys, as in London to Kings Lynn, the Queen travels in an ordinary train in first class; long journeys, that's done by plane. So I wonder what's the royal train for.