A GA SINGLE ENGINE CFI FLIES INTO ICING CONDITIONS AND RECEIVES VECTORS FROM ZDV CTLR FOR A LNDG AT COS.

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OBTAINED WX BRIEFING 2 HRS BEFORE FLT FROM TULSA; OK; TO COS. FORECAST CLR; 1 HR E OF LAMAR; SKIES BECAME CLOUDY. CALLED FLT WATCH 20-30 MI E OF LAMAR. HAD TROUBLE HEARING. COS; IFR WITH 1000 FT CEILING. CALLED ZDV AND RECEIVED IFR CLRNC TO COS; CLBED TO 9000 FT IN THE CLR. SLOW SPD; HEADWIND ABOUT 100 KTS. ENTERED CLOUD ABOUT 25 NM FROM COS (VOR). STARTED PICKING UP ICE; DID NOT REACT. LOOKED OUT AND THOUGHT; 'THAT'S NOT VERY MUCH ICE.' AIRPLANE STARTED TO SLOW DOWN AND I COULD NOT MAINTAIN ALT. REALIZED I WAS CLOSE TO A STALL; SPD ABOUT 80 KTS AND HANDLING POORLY. ADVISED ATC ABOUT ICE AND COULD NOT MAINTAIN ALT. ATC GAVE ME A TURN TOWARD LOWER TERRAIN (S) AND ALSO TOWARD ARPT. AIRPLANE CONTINUED TO DSND; ALL I COULD DO. BROKE OUT OF CLOUDS AND ATC VECTORED ME TO ARPT (STRAIGHT AHEAD). LANDED WITHOUT INCIDENT. I COULD NOT HAVE FLOWN EVEN A FEW MI FURTHER. WHAT STRIKES ME IS THAT I CONTINUED TO FLY INTO DANGER; HOPING I COULD COMPLETE THE APCH. IT WAS IN MY HEAD THAT I HAD TO FOLLOW ATC'S INSTRUCTIONS; AND I WAITED FOR ATC TO DIRECT ME OUT. IT WAS LIKE I WAS LULLED INTO TAKING NO ACTION. IT WAS A RPT TO ATC BY AN INCOMING AIRLINER OF ICING THAT TRIGGERED ME TO RPT ICING ON MY ACFT.