THE STUDENT PLT WAS PRACTICING LANDINGS ON RWY 7 & COMPLETED 1 SUCCESSFUL LANDING. HE REPORTED THAT ON THE 2ND APPROACH, A GUST OF WIND BLEW THE ACFT TO THE LEFT, SO HE MADE A GO-AROUND. A 3RD APPROACH WAS MADE WITH THE ACFT LINED UP SLIGHTLY TO THE LEFT OF THE RWY CENTERLINE. THE PLT REPORTED THAT AT AN ALTITUDE OF 5 TO 10 FT AGL, A GUST OF WIND WAS ENCOUNTERED AGAIN, WHICH BLEW THE ACFT TO THE LEFT OF THE RWY & OVER THE GRASS. HE ELECTED TO GO-AROUND AGAIN. HE STATED THAT HE APPLIED FULL POWER, PUSHED THE CARB HEAT OFF, BEGAN 'MILKING' THE 20 DEG OF FLAPS UP, AND ENTERED A SLIGHT CLIMB WITH A SLIGHT RIGHT BANK. THE RIGHT BANK WAS REDUCED WHEN HE FELT THAT THE RATE OF CLIMB WAS INSUFFICIENT. HE REPORTED THAT THE ACFT WAS BLOWN INTO TREES ON THE LEFT SIDE OF THE RUNWAY. WITNESSES ESTIMATED THAT THE WIND WAS VARIABLE FROM 070 TO 140 DEG AT 10 KTS. THE 1850 EDT WIND AT COLUMBIA, SC (7 MI WEST) WAS 180 DEG AT 12 KTS.