At Palguín Alto, near Termas de Palguín [1], the German-run Rancho de Caballos offers a series of three-hour to 10-day riding tours of the backcountry in and around Parque Nacional Villarrica [2] for about US$75 per person per day.
In addition to tours, Rancho de Caballos (Casilla 142, Pucón [3], tel./fax 045/441575, www.ranchodecaballos.com [4]) provides simple cabaña accommodations (US$12 pp with breakfast).
Links:
[1] http://www.moon.com/destinations/chile/sur-chico/pucon/sights-and-recreation/hot-springs
[2] http://www.moon.com/destinations/chile/sur-chico/pucon/sights-and-recreation/parque-nacional-villarrica
[3] http://www.moon.com/destinations/chile/sur-chico/pucon
[4] http://www.ranchodecaballos.com