I've experienced a very similar problem with my now 3 year old gelding. I bought him as a weanling and put him out to pasture with our five older horses. The older horses kept him in his place but the goats, which have free range over our 200 acres, proved just the challenge he wanted: perfect for chasing!
That was bad enough but his next target was the weanling heifers that we moved to his side of the farm during breeding season.
This spring is the first time he seems to have settled enough to leave the goats alone as the move across his pasture space. Who knows what will happen when the heifers move back over this summer!
Ultimately we resorted to putting him in the barn during the hours that the goats were in his space. It has never been an ideal solution, having to stop everything and go move one horse, but it's gotten us by.
Honestly, I've yelled at him, I've chased him back and he does respect people but when he's alone in the pasture and he thinks no one is looking it's pretty hard to stop him.
Time, honestly, and patience and simply protecting our other livestock are the route we've taken. I hope that we've reached a turning point with him and that he's matured enough to give up his games. We'll see!