The mane is supposed to lay on the right for eventing. But it doesn't REALLY matter. Both of my eventers have their manes on the left ( it's just easier to let it go it's way when it's a shire double mane! I'm just thankful it's on one side!) and I have never had anyone tell me that I need to change it.
Some eventers, you can't tell because they have the horse's mane so short that it stick straight up. Makes it easier to braid.
When you get to the upper levels, most of the professionals have their horse's manes on the traditional right side.