Swan Mountain Outfitters (877/888-5557) runs horseback rides in the park. Rides leave from corrals at Apgar [1] (406/888-5010) and Lake McDonald [2] (across the road from the lodge, 406/888-5121), and range from a $32 one-hour amble to a $135 daylong ride to Sperry Chalet. Call for specific destinations and departure times.
Links:
[1] http://www.moon.com/destinations/montana/glacier-national-park/lake-mcdonald-valley/sights/apgar
[2] http://www.moon.com/destinations/montana/glacier-national-park/lake-mcdonald-valley/sights/lake-mcdonald