On May 16, 1997, approximately 1730 mountain daylight time, a Cessna T207A, N51SA, operated by Scenic Airlines Inc. of Page, Arizona (a 14 CFR 135 on-demand air taxi certificate holder), was substantially damaged when it was struck by a galloping horse during landing at privately-owned Monument Valley Airstrip, Monument Valley, Utah. The commercial pilot, who was the airplane's sole occupant, was not injured. Visual meteorological conditions prevailed and a company visual flight rules (VFR) flight plan had been filed for the 14 CFR 91 flight, which originated at Kayenta, Arizona. The pilot reported that the airstrip was clear during his approach. He stated that after an uneventful touchdown, a herd of 5 to 7 horses appeared approaching the strip from the left at a full gallop, and that the lead horse was on a collision course with the aircraft. The pilot stated that a go-around was not feasible at that point, and that he therefore attempted to veer to the right "as much as runway width would allow" (the airstrip runway is 40 feet wide.) Despite the pilot's attempt to avert the collision, the lead horse contacted the aircraft at a full gallop, damaging the empennage and horizontal stabilizer. The aircraft did not depart the runway during the event. The pilot reported that following the event, the horse continued galloping down the runway "with no apparent break in stride...." The open-range airstrip lies partly on a Navajo Indian reservation. The portion of the airstrip which lies on the reservation is not fenced due to tribal restrictions. The operator reported that at the time of submission of its accident report, negotiations were underway between the airstrip owners and the Navajo tribe, and that the airstrip owners hoped to fence the runway in after a settlement was reached with the tribe.