Summertime trail rides are available from the corrals at Mammoth Hot Springs [1], Canyon Village [2], and Roosevelt Lodge [3]. These cost $38 for one hour or $58 for a two-hour ride. Kids must be at least eight years old and 48 inches tall, and there is a 250-pound weight limit, much to the relief of the horses.
Roosevelt also has stagecoach rides ($12 adults, $6 ages 3-11) several times a day in the summer. In addition, Old West dinner cookouts at Roosevelt [4] combine a horseback or wagon ride with a filling steak dinner.
For details on trail rides, contact Xanterra Parks and Resorts (307/344-7311 or 866/439-7375, www.yellowstonenationalparklodges.com [5]). Several outfitters provide backcountry pack trips inside Yellowstone; get a list from Park Service visitor centers (307/344-7381, www.nps.gov/yell [6]).
Links:
[1] http://www.moon.com/destinations/yellowstone-grand-teton/yellowstone-national-park/sights/mammoth-hot-springs
[2] http://www.moon.com/destinations/yellowstone-grand-teton/yellowstone-national-park/sights/grand-canyon-the-yellowstone
[3] http://www.moon.com/destinations/yellowstone-grand-teton/yellowstone-national-park/sights/tower-fallroosevelt-lodge
[4] http://www.moon.com/destinations/yellowstone-grand-teton/yellowstone-national-park/restaurants-and-food
[5] http://www.yellowstonenationalparklodges.com
[6] http://www.nps.gov/yell