Farmville's stable expansion is here. It's not very generous. You need to accumulate 10 each of the five stable parts to add 5 (five) horses. And then you can expand again, so save the extras. Farmville doesn't tell anyone in advance that you can only add five horses at a time. If I find out what the limit is, I'll let you know. For the number of horses I have, I may be accumulating parts for the next two years.
Warning - people are complaining that they have suddently lost things like Provencal gates, apparently related to the stable expansion. Mine is still there, but my virtual dogs stopped doing tricks. They just blink for a split second when they are supposed to roll over or play dead or shake. Real dogs are harder to train, but they stay trained. Doggone.