However, I have asked many judges and they always say it doesn't matter. So, who wrote the rule I'll never know but after years of trying to train manes over and failing, I for one have given up and now let horse sport his mane on the left.
It is meant to lay to the right. For some reason, I have always believed it dates back to medieval times, when knights rode horses. Most people are/were right handed, so stopped the mane getting in the way when they drew their sword.