Can Foals Do Any Riding Style?

If a foals parents are good at barrel racing the foal is not 'always' good at barrel racing. Just like humans, horses can inherit genes from their parents which make them just like them, or not at all. My mare was from aa line of champion halter and pleasure horses - she competes in barrel racing and does fine. A horse can do anything you want it to do, within reasonable limitation, you may just have to work at it more if the horse is not 'built' for a certain event, such as teaching a lazy horse to game.