On February 18, 2004, about 1400 central standard time, a Piper PA-22-135, N3419A, operated by a commercially rated flight instructor, sustained substantial damage on impact with a snow bank during landing roll at Memphis Memorial Airport (03D), Memphis, Missouri. The instructional flight was operated under 14 CFR Part 91. Visual meteorological conditions prevailed at the time of the accident. The flight instructor and student pilot sustained no injuries. No flight plan was on file. The flight originated from the Southeast Iowa Regional Airport (BRL) near Burlington, Iowa, about 1300, and was stopping at 03D for fuel en route to its final destination of Freeman Field Airport, near Junction City, Kansas. The Certified Flight Instructor (CFI) stated: We departed Burlington, Iowa at approximately 1300 hours enroute to Memphis, MO for refueling in order to make it back to Junction City, KS. The pilot that took us to Burlington was already on the ground at Memphis and stated that his landing was ok and he suggested runway 12, which concurred with the windsock. The winds aloft were strong and so my student pilot turned the aircraft over to me before short final. Upon descending to short final[,] the winds became light and so we landed, slightly right of the center line with very little aileron or rudder input. After rolling out for an unknown distance and before I could tell my student to start applying some light braking, a gust of wind hit the right side of the aircraft, lifting the right wing and pushing the tail to the left. The yoke was full aft and to the right and at that point I put in full left rudder to correct the direction of the roll out. The right wing became level but we were approximately 2 feet off the runway with the right main gear in the snow which had been pushed off the runway. At this point we were heading down the runway except for the right main gear which was still in the snow. Without brakes on the right side for assistance[,] we continued down the runway edge for approximately 40 feet before the right main gear either compacted with snow or hit some frozen snow making the aircraft tip forward [and] over on the windshield. To the south of the runway the terrain had some small hills, trees and farther south was a lake. The runway was in good shape. The pilot reported no mechanical malfunctions with the airplane. His safety recommendation was the installation of foot brakes on the right crew station to assist with directional control. At 1355, the recorded weather at Kirksville Regional Airport (IRK), approximately 26 nautical miles southwest of the accident airport, near Kirksville, Missouri, was: Wind 210 degrees at 18 knots gusting to 27 knots; visibility 10 statute miles; sky conditions clear; temperature 9 degrees C; dew point 1 degree C; altimeter 30.13 inches of mercury. Remarks: Peak winds 210 degrees at 28 knots at 1342. At 1353, the recorded weather at Ottumwa Industrial Airport (OTM), approximately 41 nautical miles north of the accident airport, near Ottumwa Iowa, was: Wind 220 degrees at 16 knots; visibility 7 statute miles; sky conditions clear; temperature 7 degrees C; dew point -1 degree C; altimeter 30.09 inches of mercury.