A couple of weeks ago we were able to go visit Royal Creek Ranches in Rush Valley, Utah. They were offering rides through their elk herd with hot cocoa & cookies after. It was really neat to get so close to the animals. They also do events, retreats, weddings, etc there! They have accommodations to stay in as well. Really neat place & we enjoyed our time there. I believe they do the elk herd rides yearly, so be on the lookout.
More info here:
Utah County Homes, The Bennetts 