B737-800 CREW ENCOUNTERED SEVERE WINDSHEAR AND MODERATE TURB CLBING OUT OF IAH; AT FL370.

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DEPARTING IAH; WE WERE ADVISED BY DEP CTL THAT PREVIOUS FLTS HAD DEVIATED S OF OUR PLANNED RTE DUE TO WX. THE FLT ATTENDANTS WERE BRIEFED TO REMAIN SEATED WITH THEIR SEATBELTS FASTENED UNTIL FURTHER NOTICE. A PA WAS MADE TO THE PAX ADVISING THEM TO REMAIN SEATED WITH THEIR SEATBELTS FASTENED FOR THEIR OWN SAFETY; DUE TO THE WX. APPROX 10 MI S OF DRAGS; CLBING THROUGH FL370; THE ACFT BEGAN TO PITCH UP AS THE AIRSPD PREDICTIVE TREND ARROW MOVED WELL ABOVE VMO/MMO. THIS WAS FOLLOWED BY THE OVERSPD CLACKER. THE AUTOPLT REVERTED TO CTL WHEEL STEERING AND WAS DISCONNECTED. ATTITUDE WAS MAINTAINED AFTER LOWERING THE NOSE; AND THE AIRSPD PREDICTIVE TREND ARROW MOVED BELOW THE BOTTOM FOOT ON THE AIRSPD INDICATOR; FOLLOWED BY A SHORT STICK SHAKER. THE TIME FROM CLACKER TO STICKSHAKER WAS SECONDS. THE ENTIRE SEVERE PORTION OF THE EVENT WAS APPROX 20-30 SECONDS; WITH MODERATE TURB CONTINUING FOR APPROX 5 MINS. QUERIED THE CABIN AND FOUND NO RPTS OF INJURIES OR OTHER PROBS. NOTHING WAS SEEN TO HAVE FALLEN FROM ANY OF THE OVERHEAD BINS. CONTINUED TO MIA FOR UNEVENTFUL APCH AND LNDG. REQUESTED THAT MAINT INSPECT THE ACFT DUE TO THE SEVERITY OF THE PITCHING OF THE ACFT. BOTH THE CAPT AND FO WX RADAR WERE BEING UTILIZED BEFORE; DURING; AND AFTER THE EVENT. SUPPLEMENTAL INFO FROM ACN 578668: LOCATION: 10 MI S OF DRAGS. DEPARTING IAH WE WERE ADVISED THAT FLTS HAD BEEN DEVIATING S OF COURSE DUE TO WX ON OUR RTE OF FLT. WE CLBED TO FL370 AND WERE IN THE TOPS OF THE CLOUDS WITH BLUE SKY ABOVE. OUR WX RADAR WAS ON AND INDICATED WX ALONG OUR RTE OF FLT. WE ASKED ATC FOR A DEV S OF COURSE AND ASKED IF THERE WAS ANY RPTED TURB ON OUR RTE. WERE INFORMED THAT THERE WAS NONE RPTED. WE DEVIATED S OF COURSE AND WELL CLR OF WX. THE CAPT HAD ADVISED THE FLT ATTENDANTS PRIOR TO DEP THAT THERE MIGHT BE TURB EARLY IN THE FLT AND TO REMAIN SEATED UNTIL WE CALLED THEM. ABOUT 10 MINS PRIOR TO THE EVENT; HE CALLED THEM AGAIN AND SAID TO REMAIN SEATED BECAUSE THERE WAS SOME WX AHEAD AND HE ALSO MADE A PA FOR THE PAX REGARDING THE WX AND THE POSSIBILITY OF TURB AHEAD. AT THAT POINT WE HAD ONLY ENCOUNTERED LIGHT CHOP AT FL370. WE DECIDED TO CLB TO FL390; IN HOPES OF GETTING ABOVE THE TOPS OF THE CLOUDS. WE WERE ABOUT 10 MI S OF DRAGS INTXN AND BEGINNING OUR CLB WHEN WE ENCOUNTERED MODERATE TURB AND THEN WHAT CAN ONLY BE DESCRIBED AS A WINDSHEAR ENCOUNTER. THE AIRSPD PREDICTIVE TREND ARROW MOVED ABOVE VMO/MMO; FOLLOWED BY THE OVERSPD CLACKER. THE AUTOPLT'S PITCH BAR REVERTED TO CTL WHEEL STEERING AND WAS DISCONNECTED. THE AIRSPD THEN MOVED IN THE OPPOSITE DIRECTION DECREASING TO STICK SHAKER. THIS ENTIRE ENCOUNTER LASTED LESS THAN 30 SECONDS.