The flight instructor reported that he and the student pilot departed the short turf runway with a low fuel load to practice landings at another airport. The flight instructor planned to refuel midway through the flight but forgot to stop for fuel, despite observing that fuel quantity gage indications were low during the flight. While the airplane climbed out during a go-around, the engine lost power due to fuel exhaustion. The flight instructor made a forced landing and the airplane impacted trees. The airplane sustained substantial damage to both wings. The flight instructor reported that there were no mechanical malfunctions or failures that would have precluded normal operation. The flight instructor attributed the inflight fuel planning error to a lack of recent flight instructor experience and the distractions of a challenging training environment.