PRACTICE INSTRUMENT FLT ENCOUNTERS NUMEROUS PROBLEMS RESULT OF ICING AND ADVERSE WX CONDITIONS.

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I CALLED FSS AND WAS TOLD THAT IT WOULD BE RAINING BTWN XC00 AND XG00 LCL TIME AND THE FREEZING LEVEL WOULD BE 6000' MSL. THE TEMP HAD RAISED FROM 32 DEGS TO 40 DEGS OVERNIGHT. XC15 I ARRIVED AT RFD AND HELPED PULL SMA FROM ITS HANGAR AFTER GETTING SMA OUTSIDE THE PRECIPITATION STARTED BRIEFLY AS SLEET THEN CHANGED TO RAIN. WE TOOK OFF INTO LIGHT TO MODERATE RAIN AND A TEMP OF 37 DEGS. DURING CLBOUT I HEARD A PIREP PUTTING THE FREEZING LEVEL FROM 4000 TO 7000' MSL (TEMP INVERSION). AS THE PIC FLEW SMA UNDER THE HOOD I WATCHED FOR TFC AND MONITORED THE OAT AND CHKED THE AIRFRAME FOR ICE. WE COMPLETED ONE APCH AND CLBED BACK TO 2500' MSL; RECEIVING RADAR VECTORS; WHEN THE AIRSPD INDICATOR WENT TO 0. THE PIC ADVISED ATC AND RECEIVED VECTORS FOR A VISUAL APCH TO RWY 12 AT RFD. THE PIC OPENED THE ALTERNATE STATIC PORT. I LOCATED AND TURNED ON THE PITOT HEAT. AFTER A FEW MINS THE AIRSPD INDICATOR STARTED TO WORK AGAIN AND I SHUT THE ALTERNATE STATIC PORT. ATC BECAME QUITE INSISTENT THAT WE STAY AT 2500' MSL (MINIMUM VECTORING ALT). THIS IS 950' ABOVE ANY OBSTRUCTION IN AREA. DURING THIS TIME WE CONTINUED TO PICK UP MORE ICE AND THE WINDSHIELD STARTED TO COAT OVER. DEFROSTERS WERE ON. RETURNING TO RFD THE PIC BECAME DISTRACTED LOOKING FOR RFD AND STRAYED OFF ATC'S VECTOR. UPON LNDG WE WERE GIVEN A PHONE # TO CALL. WE CALLED THE # AND WERE CHEWED OUT FOR STRAYING FROM COURSE AND ALT AND WAS ADVISED THAT WE WERE BEING RPTED TO GADO AS THE ATC MAN WAS CERTAIN THAT WE VIOLATED SOME FAR; BUT HE WASN'T SURE WHICH ONES. I WOULD HAVE NEVER STARTED ON A CROSS COUNTRY FLT ON THAT DAY BUT WAS SURE WE COULD STAY OUT OF TROUBLE BY STAYING NEAR RFD. DOES THE OAT FUNCTION PROPERLY WITH THE AIR INTAKE TAPED OVER? NORMAL WINTER PRACTICE. DOES OPENING AND CLOSING THE ALTERNATE STATIC PORT AFFECT THE TRANSPONDER RETURN? WE DIDN'T RECEIVE A BAROMETRIC UPDATE UNTIL IT HAD FALLEN .03. WHY DID ATC INSIST THAT WE STAY IN FREEZING CONDITIONS INSTEAD OF GIVING US A LOWER ALT? WE SHOULD HAVE INSISTED ON A LOWER ALT. THE ICE ACCUMULATED ON THE UPPER SURFACE OF THE WING AND COULDN'T BE SEEN. ALTHOUGH A SLIGHT AMOUNT HAD ACCUMULATED ON THE TAIL AND WING STRUT IT BLEW OFF AT 2000' MSL; BUT THE ICE REMAINED ON THE WING (APPROX 3/8'). I THINK THE PRACTICE OF INTIMIDATING PEOPLE WITH ENFORCEMENT ACTION WILL BE COUNTERPRODUCTIVE; AS I WILL BE VERY HESITANT TO ADVISE ATC AGAIN IF I HAVE ANOTHER PROB. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: FAA HAS MADE NO INQUIRY REF THE INCIDENT. ACFT WAS A FLYING CLUB ACFT. BOTH RPTR AND THE PLT WORK NIGHTS AND BELIEVE THAT IS THE REASON THE FLT WAS NOT SCRUBBED. COUNSELED ON RETURNING THE ACFT TO THE HANGAR WHEN SIMILAR CONDITIONS ENCOUNTERED. PITOT HEAT WAS NOT THOUGHT OF PRIOR TO FLT IN SPITE OF THE CONDITIONS. NO REASON WHY THE CTLR COULD NOT GIVE THEM A LOWER ALT. ADVISED THE OAT PROBABLY WOULD NOT BE RELIABLE UNDER THE CONDITIONS DESCRIBED AND THE TRANSPONDER WOULD PROBABLY BE EFFECTED BY THE ALTERNATE STATIC SOURCE.