Notes:

100% official, straight from Nintendo's Japanese FE:Fates site!

Looks like, as in Awakening, they have the same hair color as the parent they're tied to for the most part, besides the doppelgangers having their original's hair color, and a few weird exceptions, like Mitama having pink hair.

However, due to the first-gen cast having more diverse hair colors this time around, I'm pretty sure most of these second-gen hair colors won't even be possible to actually have in the game.