The Children were the greenseers and skinchangers. They were small and couldn't fight men so they used animals to fight (skinchanging). The ability to greensee is also theirs because of the weirwoods. And just because there was peace doesn't mean the Children didn't resent the hell out of men for destroying their trees and taking their land. We see it all throughout our own history, nations can hold a grudge for generations against those who conquered them. The Starks have Children blood themselves, hence the ability to warg/skinchange and greensee. When the Children gave up, their females were forced to mate with humans, passing down those abilities.