Movie where all the horses jump over a cliff, into the sea?

I've been trying to find the name of this movie for so long. I keep thinking Cate Blanchett played the lead. The man character ends up on a farm of some sort (lighthouse?) where she keeps looking at a spooky portrait of the lady who used to live there and breed with / train horses. She finds newspaper clippings detailing strange events which led to all the horses jumping over a cliff into the sea.

Please help :-)