B737-300 CREW ABORTED TKOF AFTER THE TKOF WARNING HORN SOUNDED. THE CREW HAD NOT RESET THE STABILIZER TRIM FROM THE DEICE POS.

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ON LEG 5 OF A 6-LEG DAY; WE ARRIVED IN ALB AFTER HOLDING FOR THE RWY TO BE PLOWED. WE WERE LATE DUE TO THE HOLDING AS WELL AS DEICING EARLIER IN THE DAY WHEN WE ORIGINATED FROM BAL. WHILE AT THE GATE IT WAS SNOWING HEAVILY. THE SNOW REMOVAL CREWS BEGAN CLOSING THE RWY EVERY 45 MINS OR LESS TO PLOW THE RWY. WE HAD TO REMOVE 30 PAX FOR OUR DEP BECAUSE OF THE CLUTTER ON THE RWY CAUSING A TKOF WT LIMIT. THE VISIBILITY WAS HOLDING STEADY AT 1/4 MI WITH SNOW. THE TKOF WT ISSUE TOOK QUITE SOME TIME AS WELL AS TRYING TO PLAN OUR TKOF WITH RESPECT TO THE RWY CLOSURES. WE PUSHED OFF THE GATE 1 HR AND 10 MINS AFTER BLOCKING IN. WE WERE DEICED BY CONTRACT DEICING USING TYPE 1 FLUID FOLLOWED BY TYPE 4 FLUID. WHILE WE WERE STILL DEICING; TWR BEGAN PLANNING THE NEXT RWY CLOSURE. WE INFORMED THEM WE WERE ALMOST FINISHED DEICING AND THEY SAID THEY WOULD LET US DEPART BEFORE CLOSING THE RWY AGAIN. WE FINISHED DEICING; RAN THE PRETKOF CHKLIST AND TAXIED TO THE RWY. ANOTHER ACFT WAS WAITING TO DEPART AND THE SNOW REMOVAL EQUIP WAS JUST OFF TO THE SIDE OF THE TXWY AT THE THRESHOLD. THE OTHER ACFT WAS CLRED FOR TKOF AND CAUSED NEAR WHITEOUT CONDITIONS BEHIND IT ON TKOF ROLL. AFTER THE BLOWING SNOW SETTLED WE WERE CLRED FOR TKOF. THE 'BELOW THE LINE' PORTION OF THE CHKLIST WAS ACCOMPLISHED AND PWR WAS APPLIED TO BEGIN THE TKOF. SHORTLY AFTER BEGINNING THE TKOF ROLL THE TKOF WARNING HORN SOUNDED AND WE ABORTED THE TKOF. WE ONLY REACHED ABOUT 10 OR 15 KTS. WE DISCOVERED THE HORN SOUNDED BECAUSE THE TRIM WAS STILL SET FOR DEICING. AFTER EXITING THE RWY WE BRIEFLY DISCUSSED THE ISSUE. WE THEN RE-ACCOMPLISHED THE WHOLE PRETKOF CHKLIST. WE WERE AGAIN CLRED FOR TKOF AND THE SUBSEQUENT TKOF AND DEP WERE UNEVENTFUL. ALTHOUGH WE WERE WORKING SEVERAL ISSUES AND DEALING WITH PENDING RWY CLOSURES; I NEVER FELT RUSHED AT ANY POINT DURING OUR GND OPS; INCLUDING THE ACCOMPLISHING OF CHKLISTS. I DO NOT THINK THERE WAS ANY ONE THING THAT CAUSED OUR ERROR. I DO BELIEVE THERE WERE MANY DISTRS ALONG THE WAY; ANY ONE OF WHICH MAY OR MAY NOT HAVE PLAYED A ROLE. I DO THINK WE WERE BOTH A BIT DISTR BY THE DEP OF THE OTHER ACFT AND THE SNOW REMOVAL EQUIP JUST PRIOR TO OUR TKOF. THAT WAS OUR LAST CHANCE TO CATCH THE TRIM ERROR WITH THE THRUST LEVER RUN-UP CHK. ONE WAY TO PREVENT THIS FROM OCCURRING AGAIN IN THE FUTURE COULD BE TO MAKE THE THRUST LEVER (CHK OF THE TKOF WARNING HORN) A CHALLENGE AND RESPONSE ITEM; EITHER BEFORE OR AFTER THE 'BELOW THE LINE' PORTION OF THE CHKLIST.