The pilot reported that prior to landing on a dirt road; he overflew the area, noting a group of cows nearby prior to entering a left-hand pattern for his intended landing area. During the landing flare, the pilot observed a cow approaching the flight path of the airplane from his left to right and attempted to maneuver the airplane to avoid a collision. Subsequently, the left main landing gear struck the cow and the airplane immediately veered to the left. Despite the pilot's control inputs, the airplane continued to the left, landed hard, bounced, and settled back onto the ground. Examination of the airplane by the pilot revealed structural damage to the left elevator, horizontal stabilizer, and engine firewall. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.