[Linny]

I'll ask a friend with some connection to Stonerside.
While I doubt it was McNair, I'm fairly sure that at least in the case of many of the horses there is thought given to where each horse will have the best chance to thrive.
I have no idea at what age the homebreds are sent abroad. If they were raised and broken to saddle here, my guess is that those overseeing the process would be involved in deciding which horses went to which division.

I have spoken with some people who have horses with several trainers. They do assess the horses and try to suit them. A delicate filly for example may not stand up to one trainer's regimen but could thrive in another's.