The official website has some explanations for why they picked it and what a rigorous shoot it was.
(Arabian-Horse-World, April 1978)
Film production divided into two distinct halves as locations were settled. Sardinia was chosen for the island sequences of the film because of the spectacular remote areas of its coast; and Toronto, Canada, was selected as a perfect match for the eastern seaboard of the United States in the late 40's.
[filming was completed over a nine-week period, and despite the obstacles presented by the difficult terrain, director Carroll Ballard feels the varied and unusual beauty of Sardinia captured on film creates a spectacular backdrop for the movie.
The side of Sardinia that was used for the beach scene's is called the Costa Smeralda because the water is emerald green .... so clear you can see all the way to the bottom, it's simply beautiful. The sand is spotless with little flowers popping up thru the sand. NO vehicles are permitted on those beaches and they are anal about trash. Cows and sheep have the right of way ... no kidding, cows just wonder around free in that part of the island. Sardinia is about an hour's flight from Rome. The homes that are high on the hills overlook the beaches b/c of the strict ruling about keeping the beaches natural and away from the construction.
I watched them shot seven days of the beach scenes ... I didn't see other horses or stand-ins ... not sure where they had them but the only horse I saw and met was Cass Ole .... like I said in my other post, the biggest problem was the lighting and sun reflecting off the water........ making Cass Ole's coat color a problem. I didn't get a chance to see the movie until years later ....... I had pictures of all this but God only knows where the hell they are now. I mean who knew I would one day own an Arabian and want those pic's for reference. :-(