Headline is a little misleading. Horses and sage grouse actually evolved together before horses were pushed to extinction (likely by overhunting combined with climate change).
The issue is overly large and dense herds—or in other words, a lack of large predators that would keep horse numbers in check in a more complete and functioning ecosystem. This problem may be solved by reintroductions and better management of large predators like wolves, grizzlies, and mountain lions.