I've actually had some that were almost totally "done" growing by 18mos. From what I've observed, it varies a lot depending on bloodlines. But, I've had a number of horses who were all but done growing by 18mos, including one of my stallions... it seems so far that his offspring may follow the same trend.
That's why AMHA voted in that horses couldn't be permanently registered until age FIVE..........Too many old time breeders were withholding feed to their pregnant mares to keep their foals tiny, and then the foals were withheld proper food which stunted their growth. Eventually the foals did "catch up" in their growth but it took a couple of extra years.......Another huge factor is feed. If a young horse isn't getting the proper food it needs to grow, it's going to take it a lot longer to get to its mature height.