On June 3, 1999, at 1730 central daylight time, a Piper PA-38-112, N4273E, sustained substantial damage when it impacted the ground during a go-around at May Field, Houston, Texas. The certified flight instructor and his student were not injured. Visual meteorological conditions prevailed for this local area instructional flight operating under Title 14 CFR Part 91 and no flight plan was filed. The flight originated from David Wayne Hooks Field, Spring, Texas, at 1620. According to the flight instructor, the student was flying and a crosswind caused him to lose control. During the attempted go-around, the aircraft struck the ground. The flight instructor reported he had 365 hours total flight experience with 25 hours as a flight instructor and 24 hours as a flight instructor in the accident make and model aircraft. The student reported he had 160 hours total flight experience with 17 hours in the accident make and model aircraft and 4 hours as pilot in command in the accident make and model. The closest weather reporting station was at David Wayne Hooks Field, Spring, Texas located approximately 4 miles from the accident site. Weather at that facility at 1753 indicated the winds were from 160 degrees at 10 knots with no gusts reported. The flight instructor reported the winds at May Field were from 230 degrees at 10 with gusts to 20 at the time of the accident. Both the instructor and the weather station indicated there were scattered clouds at 4,000 to 5,000 feet. The landing was being made on runway 17.