Edgar,

I see that you got an answer to the current question. I have a question for you though;

IDN   Name    Parent   Gender
1     Silver    3      Horse
2     Golden    3      Mare
3     Silverado 0      Horse

How will you handle when Silver and Golden have another child? Or when Golden has a child with some other stallion? I would suggest that you do something like this;

Horses
IDN   Name      Gender
1     Silver    Horse
2     Golden    Mare
3     Silverado Horse

Heritage
IDN    Mare     Horse   Child
1       2        1       3

This way each child born has a record in Heritage that shows its parentage. Parents may parent multiple children with the same or different partners.
Limitations in the original design are gone. Besides the dealing with parents and children is greatly simplified as it is no longer a table self join to get the data.