You can always cheat and use NRAAS master controller
If you happen to have it.. Nraas > Master Controller > Intermediate (pretty sure, anyway) > Instant Baby > Home Lot (If you own the sire.. You can have two mares spawn a baby this way too) *If you don't own the sire, you can scroll down the list and there should be "Species" I believe? And you can find the available horse you want that way
There's also a Pollinate option somewhere, and I've accidently pollinated a stud >_< so.. we'll see what happens there.
Instant baby has no Gestation period, it just spawns the foal. And it'll ask you how many foals to have, I've only gone up to 3 at a time (Using it so I can have Pick of the Litter, really xD) and you can pick the genders - all fillies/females, colts/males, or let the game choose.