I keep trying to breed my horses.  I select a mare on the list and it refreshes but no mare appears on the list. 

I think it's because your stallions are set to Public stud. Try changing the "available for stud?" to "No" and then request the breeding with your mare.

I let the programmer know :).

Okay I'll try that and report back if it works.  Thank you.

Try now (on public stud)