A DA200 CREW DEPARTED WITH THE PITOT TUBE COVERS INSTALLED AND AFTER TKOF HAD NO PITOT DRIVEN INSTS EQUIP. ATC DECLARED AN EMER AND FLT RETURN TO DEP ARPT.

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AFTER TKOF; MULTIPLE IRREGULARITIES SHOWED UP AND CONTINUED TO SHOW UP AS WE DEPARTED AND WERE CLBING TO ALT. I HAD NO AIRSPD INDICATIONS ON THE PLT'S SIDE EXCEPT IN REVERSION; ADC #1 SEEMED TO HAVE FAILED; THE YAW DAMPER LIGHT CONTINUED TO COME ON AFTER RESET; AILERON FEEL ANNUNCIATOR LIGHT WAS ON STEADY; AILERON ZERO ANNUNCIATOR LIGHT WAS CYCLING ON AND OFF. SPECIFICS OF OCCURRENCE: AFTER TRYING TO ASSESS OUR PROB AND THINKING WE HAD TAKEN IN WATER IN A CRITICAL AREA; DURING THE PROCESS OF THAWING OUT THE ACFT FROM A PREVIOUS DAY'S 3 INCH SNOWFALL; I ELECTED TO RETURN TO ZZZ. CTR ADVISED THAT DUE TO THE PROBS WE WERE ENCOUNTERING AND THE HVY TFC AREA; THEY WERE GOING TO ISSUE AN EMER FOR US TO EXPEDITE OUR ARR BACK TO ZZZ; WE RETURNED AND LANDED NORMALLY. POSTFLT FOUND OUR PLT SIDE PITOT TUBE STILL HAD THE PITOT COVER INSTALLED. ACFT WAS REDISPATCHED AND CONTINUED TO DEST. AS EMBARRASSING AS THIS IS AND IT IS NO EXCUSE AND NONE IS INTENDED; OUR PITOT COVERS WERE MISSING THE RED 'REMOVE BEFORE FLT' FLAGS AND CONSEQUENTLY THESE COVERS; MADE OF METAL; JUST SLIGHTLY LARGER THAN THE PITOT TUBE ITSELF AND AS WE NOW KNOW; ARE EASILY OVERLOOKED.