My unicorn, Sable, had her nooboo and he is a normal foal named Ricochet. He didn't have any skill points at birth, not sure if he will gain them when he grows up or not. He is white like his father and has a black mane and tail like his mother. He looks to be quite stunning when he is grown.
I also found a white male unicorn in the wild (I'm forgetting his name at the moment), so I let my white female unicorn go. I can confirm for the 3 unicorns I've captured the male has lion's tail and beard and the females have no beard and a regular horse tail. I'm excited to breed my 2 unicorns, but I have to wait for Sable's foal to mature so I can sell him. I'm playing on long lifespan so I may give in and age him up via cheats, I haven't decided yet.