The certified flight instructor (CFI) and the student pilot had conducted a night visual flight rules instructional flight and were returning to their home, non-towered airport. The student pilot set up for landing on runway 1, and according to the CFI, they looked carefully for wildlife on and near the runway throughout the approach and flare, and did not observe any. During the flare, a deer ran onto the runway from the grass adjacent to the left runway edge, and struck or was struck by the left horizontal stabilizer. The pilots maintained control of the airplane, and the touchdown and rollout were uneventful. The stabilizer was substantially damaged, and the pilots were uninjured. According to the CFI, this was the third deer strike at that airport in as many years. The Federal Aviation Administration (FAA) Airport/Facility Directory stated that wildlife was present on and in the vicinity of the airport, and the CFI reported that a similar message was normally contained in the airport's AWOS (automated weather observing system) radio broadcast. NTSB discussions with the airport manager and personnel from the FAA revealed that deer are a known problem at the airport, and that efforts are underway to approve, fund, and install an airport perimeter fence no sooner than approximately fall 2014. Discussions with United States Department of Agriculture (USDA) Wildlife Management Division personnel revealed that the local office of the USDA was willing and able to provide direct technical assistance to the airport to explore and implement deer hazard mitigation strategies in the interim.