MULTIPLE PROBS DURING CLB IN ICING CONDITIONS LEADS TO DIVERSION AND PRECAUTIONARY LNDG.

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ON CLBOUT FROM DFW WE ENCOUNTERED LIGHT TO MODERATE ICING IN THE CLB. WE HAD ENG AND WING ANTI-ICE ON. AT ABOUT FL190 WE GOT A COMPARE SPD WARNING FOLLOWED IMMEDIATELY BY A STABILIZER TRIM YAW DAMPER AND AUTOTHROTTLE FAIL WARNINGS -- ALL ON THE #1 SYS. THIS WAS ALSO ACCOMPANIED BY A MAJOR SPLIT IN THE THROTTLES. I DECIDED TO DIVERT INTO TUL. WE NOTIFIED ATC OF OUR INTENTIONS; BUT I DID NOT DECLARE AN EMER. THE FO'S AND STANDBY INSTS WERE WORKING NORMALLY AND WE WERE ABLE TO FLY THE AIRPLANE NORMALLY. WE DID NOT WANT TO FLY BACK TO DFW BECAUSE THE WX AND ICING MAY HAVE BEEN THE CAUSE OF THE PROB AND TUL WAS VFR AND A MAJOR MAINT BASE. WE LANDED AT TUL WITHOUT ANY FURTHER PROB. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR SAID THAT THE PROBS ENCOUNTERED WERE CAUSED BY THE FAILURE OF A PITOT HEAT SYS THAT ALLOWED ICE BUILDUP RESULTING IN ERRONEOUS INPUTS TO AN AIR DATA COMPUTER. THE COMPUTER FED THE EFFECTED SYS. THE PROBS RESOLVED THEMSELVES AFTER DSCNT TO WARMER ALTS DURING THE ARR TO THE DIVERSION STATION.