FLC OF LGT ENCOUNTERS WINDSHEAR ON FINAL AND EXECUTES GAR. DIVERTS TO ANOTHER ARPT.

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I WAS CAPT AND THE PF ON FLT CVG TO BUF. THE WX FORECAST FOR BUFFALO ARR WAS INDICATIVE OF STRONG WINDS OF 240 DEGS AT 24 KTS WITH GUSTS TO 35 KTS. ANTICIPATED RWY WAS RWY 23 AT BUFFALO. ON ILS APCH; MODERATE TURB WAS ENCOUNTERED ALL THE WAY DOWN FINAL WITH PLUS AND MINUS AIRSPD DEVS OF 10-15 KTS. IT SHOULD BE NOTED THAT PRIOR TO THE EVENT; APCH AIRSPD WAS VREF +20-30 KTS AND PWR WAS STILL AT APCH PWR SETTING. JUST PRIOR TO TOUCHDOWN; A VERY STRONG GUST DESTABILIZED THE ACFT WITH EXCESSIVE YAW AND EXCESSIVE SINK RATE. I APPLIED GAR THRUST. THE ACFT CONTINUED TO SINK UNTIL THE MAIN WHEELS TOUCHED THE RWY IN THE PROCESS OF GOING AROUND. THE ACFT'S WINDSHEAR WARNING SYS DID NOT ACTIVATE DUE TO THE IMMEDIATE NATURE OF THE EVENT AND THE SUBSEQUENT INHIBITING OF THE SYS WHEN GAR WAS SELECTED. DUE TO RECOGNITION OF WINDSHEAR IN THE LNDG ZONE AND THE LEVELOFF TURB IN THE AREA; I DECIDED TO DIVERT THE FLT TO SYRACUSE. A PIREP WAS GIVEN TO ATC. ON THE GND AT SYRACUSE; I RECEIVED CONTINUAL WIND RPTS FROM BUFFALO TWR; RELAYED THROUGH THE FLT DISPATCHER. WHEN WINDS HAD DECREASED TO AN ACCEPTABLE LEVEL; I CONTINUED THE FLT BACK TO BUFFALO AND LANDED SAFELY.