PLT OF A MOONEY 201 GOT OFF AIRWAY AND FLT PLAN ROUTING WHILE CIRCUMNAVING TSTM WX BUILDUPS. CTLR THOUGHT THAT THE RPTR HAD INADVERTENTLY ENTERED RESTR AIRSPACE.

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WHILE ENRTE FROM DALLAS ADDISON TO BIRMINGHAM; I ASKED FOR AND RECEIVED A HIGHER ALT FROM 9000 FT TO 11000 FT. I DID THIS BECAUSE THERE WERE SOME BUILDUPS IN THE AREA AND AT 11000 FT WOULD BE ABOVE THE UNDERCAST AND WOULD BE ABLE TO SEE THEM. BTWN SQS AND IGB ON V278; I NOTIFIED ZME THAT I WOULD HAVE TO DEVIATE TO GET AROUND SOME BUILDUPS AND THIS WAS APPROVED. I TOLD THEM I WAS DEVIATING TO THE N; AND UNFORTUNATELY THEY DIDN'T SUGGEST THAT GOING S WOULD AVOID A MOA; AND I DIDN'T NOTICE IT ON THE CHART. MOST OF THE BUILDUPS WERE MINOR; SO IN ORDER TO AVOID FURTHER DEVS ( I BELIEVE I WAS 3-4 MI TO THE L OF THE CTR OF THE AIRWAY); I DECIDED TO PENETRATE A SMALLER CLOUD. AS SOON AS I DID; 3 THINGS HAPPENED. FIRST; I STARTED TO GET MODERATE TO SEVERE TURB. SECOND; I STARTED TO GET FREEZING RAIN (MY PLANE IS NOT EQUIPPED FOR ICING). AND THIRD; I GOT A CALL FROM CTR WHICH I HEARD AS SAYING SOMETHING ABOUT HAVING TO TURN R TO THE S. (I LATER LEARNED THAT CTR WAS SAYING SOMETHING ABOUT HAVING TO TAKE LOWER.) I ADVISED THAT I WAS EXPERIENCING HVY TURB AND FREEZING RAIN AND WAS UNABLE TO ACCEPT A TURN TO THE S; AND IN FACT WAS TURNING N WHERE I KNEW THE EDGE OF THE BUILDUP WAS CLOSE. CTR CALLED AGAIN; BUT AT THAT POINT I DIDN'T HAVE THE TIME TO LISTEN OR REPLY -- I WAS BUSY FLYING THE AIRPLANE. WHEN I CLRED THE CLOUD I CALLED CTR AND ADVISED WHAT HAD HAPPENED; AND THAT I WOULD NOT BE ABLE TO TURN S UNTIL I GOT AROUND THE BUILDUP; BUT FELT I COULD TURN S IF THEY COULD GIVE ME 13000 FT; WHICH THEY DID. CTR ADVISED ME I HAD ENTERED THE MOA; AND THAT THE FAA MIGHT WANT TO SPEAK TO ME WHEN I LANDED (I WAS NOT SO NOTIFIED). EVENTUALLY; I TURNED S; AND EVERYTHING STRAIGHTENED OUT. THIS WHOLE INCIDENT PROBABLY LASTED 2-3 MINS. MY ONLY RECOMMENDATION WOULD BE THAT HAD CTR SUGGESTED THAT MY DEVS BE TO THE S; AWAY FROM THE MOA; THIS PROB NEVER WOULD HAVE OCCURRED. IF HE HAD EVEN ADVISED THAT THE MOA WAS HOT; THAT PROBABLY WOULD HAVE BEEN SUFFICIENT TO HAVE ME CHK. IN ANY EVENT; WHEN I DID ENCOUNTER THE FREEZING RAIN; I FEEL THAT I WAS CORRECT TO WORRY FIRST ABOUT ESCAPING THE SIT AND THEN WORRYING ABOUT DEALING WITH ATC.