I retired some of my orig horses and I cant find them anywhere to breed with.
So i guess the answer is no, you can not continue your breeding lines, thats just killed the longativity for this game.

Another thing that bugs me with the breeding is when you breed your own horse it should be yours to controll who you wants to ride it and full controll where its gonna race.

I do like the game but if it had those features i metioned it would be the best horse racing game easily.