B737-700 FLT CREW FAILS TO CONSIDER CROSS WIND LIMITS WHEN COMPUTING TKOF PERFORMANCE DATA ON A RWY WITH REPORTED POOR BRAKING.

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THIS WAS OUR FIRST FLT OF THE DAY. ATIS IN CLE WAS RPTING WINS 330 DEGS AT 17 KTS GUSTING TO 27 KTS. THE BRAKING ACTION RPT ON THE ATIS FOR RWY 24L WAS MU 38/45/38 BUT IT HAD NOT BEEN WRITTEN ON THE ATIS SHEET SO I WAS NOT AWARE OF IT. THE RAMP WAS ONLY PARTIALLY COVERED WITH SNOW SO I EXPECTED THE RWY TO BE CLR. WHEN WE GOT TO THE END OF THE RWY; I COULD TELL THE RWY WAS ABOUT 50% COVERED WITH SNOW BLOWING ACROSS IT AND AT ABOUT THE SAME TIME; A LNDG ACFT RPTED FAIR TO POOR BRAKING. WE DECIDED TO DO A DASH PWR TKOF AND I CHANGED THE OPC TO REFLECT THIS. WE RESET THE FMC AND WERE SOON CLRED FOR TKOF. AFTER WE GOT AIRBORNE; I REALIZED I HAD NOT INPUT INTO THE OPC ANY BRAKING ACTION CONDITIONS; SO OUT OF CURIOSITY; I DID. I WAS SURPRISED AND FELT FOOLISH TO HAVE BEEN REMINDED OF THE XWIND LIMITS WITH LESS THAN GOOD BRAKING ACTION RPTED. WE WENT BACK AND CHKED THE LATEST ATIS AND WINDS WERE 330 DEGS AT 15 KTS GUSTING TO 25 KTS. SUFFICIENT FOR FAIR BRAKING BUT NOT FOR POOR. NEITHER ONE OF US COULD RECALL THE ACTUAL WINDS RPTED BY TWR WHEN CLRED FOR TKOF. DISPATCH WAS NOTIFIED BY ACARS OF THE CURRENT CONDITIONS SO THEY COULD MONITOR IT. IN ANALYSIS; THE ATIS BRAKING ACTION WAS GOOD TO FAIR AND WINDS WERE RIGHT AT LIMITS. PLT BRAKING ACTION RPT WAS FAIR TO POOR AND WINDS WERE OUT OF LIMITS FOR THIS. I FAILED TO PROPERLY CONSIDER ALL FACTORS PRIOR TO BEGINNING THE TKOF ROLL. EVEN THOUGH I FEEL THE TKOF WAS LEGAL; BARELY; I SHOULD HAVE MORE THOROUGHLY CONSIDERED ALL FACTORS BEFORE CONTINUING. IN THE FUTURE WHEN CONDITIONS ARE CHANGING; I WILL MAKE SURE I TAKE THE TIME TO ENSURE ALL FACTORS ARE PROPERLY CONSIDERED SO I CAN MAKE THE BEST AND SAFEST DECISION. ANOTHER FACTOR THAT COULD HAVE HELPED WOULD HAVE BEEN WARNINGS BY EITHER THE INBOUND CREW OR DISPATCH OF WINDS NEAR LIMITS WITH LESS THAN GOOD BRAKING ACTION.