Eventer - I do Jumper shows in my Skull Cap, and Dressage Shows in my Skull Cap, and I've been just fine. The only thing is, is that everyone knows I'm an Eventer...lol.
Skull Caps are just as ASTM approved as any other helmet, BUT the difference is, is that the reason why Skulls do not have the SOLID visor, is for safety reasons among others.
I learnt this from an Olympic Eventer - The reason why Skull Caps have covers with visors that are not solid, is incase of a fall, it's to help prevent your neck from craning too far back, causing long term damage to your spine. Where if you have a helmet with a solid visor that comes strait out from the helmet, that can cause your neck to crane back too far. *shrugs shoulders*
And, also when you are out on a CC course, you do not want a visor that limits your line of vision. You need to see your surroundings without anything hindering your line of sight, like a visor that comes strait out from your helmet.
So - if you are going to Event, use a Skull Cap :)