AN SMA PLT GOT INTO ICING WITHOUT PROPER PROTECTION.

Narrative

AFTER DEPARTING MBS ARPT; WE WERE CLRED FOR A HDG OF 210 DEGS AND 6000 FT. THERE WAS A RPTED CEILING OF 4000-5000 FT MSL; BUT NO TOP OF CLOUDS WERE RPTED. AFTER ENTERING THE CLOUDS AT 5000 FT; I HEARD 1 RPT FROM ATC OF LIGHT RIME ICE AND 1 PLT RPT OF NO ICE AT 6000 FT. AFTER GETTING TO 6000 FT AND WE DID NOT BREAK OUT ON TOP; I REQUESTED 8000 FT. UPON REACHING 7000 FT; ENG RPM REDUCED BY 500 RPM. POSSIBLY DUE TO ICE ON THE PROP; BECAUSE I COULD FEEL STRANGE VIBRATIONS. WHEN ATC ASKED FOR THE CONDITION OF ACFT; PWR RETURNED; BUT THE PLANE REFUSED TO CLB ANY HIGHER THAN 7000 FT. SO I REQUESTED A LOWER ALT TO GET OUT OF THE CLOUDS. WE GOT 5000 FT. WE WERE STILL IN THE CLOUDS. ATC GAVE US 4000 FT AND WE COULD SEE THE GND AGAIN. AFTER FLYING FOR 5 MINS AT 60 KIAS; SUDDENLY THE VIBRATION STOPPED AND IAS WENT BACK TO 110 KTS. GND SPD SHOWED ABOUT 130 KTS. WE STAYED AT 4000 FT UNTIL WE GOT BACK INTO THE SUNSHINE ABOUT 1 HR LATER. THEN WE REQUESTED 6000 FT AND WERE CLRED. ATC DID NOT ASK ABOUT CONDITION OF ACFT AGAIN AND I DID NOT VOLUNTEER. VIOLATION WOULD BE FAILURE TO MAINTAIN A CLB RATE OF 500 FPM TO REACH AN ASSIGNED ALT AND FLYING INTO KNOWN ICING. I THOUGHT THAT I COULD BREAK OUT ON TOP; BUT THE PLANE HAD OTHER IDEAS.