The pilot reported that the airplane was on final approach to the runway in dark night visual conditions with no moon illumination present. She observed that the airport lighting seemed dim and the area surrounding the runway was not illuminated. When she initiated the landing flare, she observed a white-tailed deer running across the runway from the right to the left. She initiated a go-around; however, the deer impacted the right horizontal stabilizer. During the go-around, she noticed a reduced climb performance and a right yaw, however she was able to safely control the airplane. She decided to divert to a different airport due to the possibility of additional deer being present near the runway or perhaps a dead deer on the runway. The pilot contacted air traffic control and landed at a nearby airport without further incident. The right horizontal stabilizer sustained substantial damage. The pilot reported there were no preimpact mechanical malfunctions or failures with the airframe or the engine that would have precluded normal operation. The current airport entry in the FAA Airport/Facility Directory states in the remarks section, “deer & waterfowl on and invof arpt.” According to the University of Wisconsin, white-tail deer prefer an open forest environment consisting of meadows, woodland clearings and farmland and additionally prefer low light to forage, mainly at sunrise and sunset. The accident occurred about 1 hour and 38 minutes after sunset. The publicly owned airport, which is located next to a 30,000-acre state wildlife area, does not have fencing installed to exclude deer and other mammals, nor is it required to. The FAA has published CertAlert 16-03 Recommended Wildlife Exclusion Fencing and states in part: Proper fencing is the best way of keeping deer and coyotes off aircraft movement areas. The FAA recommends a 10-foot fence with 3-strand barbed wire outriggers.