The pilot reported that he rented the accident airplane for the purpose of gaining night cross-country flight experience. He flew to two other airports and made successful landings at each airport. On the accident flight, as the airplane approached the airport, the pilot attempted to activate the pilot-controlled runway lights but was unsuccessful. He elected to continue the landing attempt to the grass runway. He stated that the landing approach was on-speed per the airplane flight manual, and he touched down on the runway but was unable to stop the airplane before it impacted trees at the end of the runway. The pilot reported that there were no mechanical malfunctions or failures of the airplane that would have precluded normal operations. The airplane received substantial damage to the left wing. The destination airport had a 3,303 ft. by 80 ft. turf runway equipped with non-standard low-intensity runway lighting. The airport manager reported that the functionality of the pilot-controlled runway lighting system was confirmed following the accident.