I have just leased 2 horses. One is still at the farm of the owner. Is this horse regaining NE because strictly speaking that is still her “home” farm? Or now I am her “owner” for the next few months, do i have to ship her to my stable to regain NE?
As long as the horse is away from a track (at a farm), it will gain NE. The horse doesn’t care if it’s your farm or the owning farm. A field is a field, in the minds of FF horses. 
Thanks for that information, I wasn’t sure how that worked. 