A C182 pilot and instructor on a cross country encountered rime ice after making several route adjustments to avoid the weather. On approach to a diversionary airport; the iced over windshield caused approach difficulties.

Narrative

Our aircraft departed ZZZ1 at XA21 with an intended destination of ZZZ2. The flight was conducted under Part 91 IFR and was filed through DUATS as ZZZ1 direct ZZZ2. Our aircraft was a 2008 C-182 equipped with G1000 avionics which included NEXRAD data uplink radar. However; this particular Skylane is not equipped with deice or anti-ice systems. Approximately 1 hour after departure; we referred to the NEXRAD radar and made the decision that a direct ZZZ2 flight would not be prudent due to winter weather that was moving through and was traveling in a southeast direction. At this time; we called Flight Watch to get a current briefing on the weather system. After our briefing; we radioed ARTCC and requested to amend our clearance to ZZZ2 via ZZZ3. This flight path carried us due east; under the south side of the impending weather. Once we neared ZZZ3; the weather system had begun moving into the area. At this point; Center requested our flight conditions; which happened to be VMC between 2 overcast layers. We once again referred to our NEXRAD system; and made the decision to amend our clearance once again to fly ZZZ2 via ZZZ prior to reaching ZZZ3. By our calculations; this would limit our exposure to the impending weather by flying through the area that was showing the least radar activity. Approximately 15 miles south of ZZZ; we encountered IMC at our present altitude of 11;000 FT MSL. This is when our aircraft started to collect light to moderate rime ice. The decision was then made to change altitudes in attempt to evade the icing conditions. Since our performance was limited; we decided to request a cruising altitude of 9;000 FT MSL. Immediately after we initialized our descent; we encountered freezing rain/SLD. The airframe as well as the windscreen started to collect ice at a very rapid rate. At this time we alerted Center of our situation and requested a descent as well as immediate clearance to ZZZ. Our request was granted and we were cleared to ZZZ no lower than 3;100 FT MSL. Center asked if we wanted to declare an emergency and since our request was granted we decided to forgo declaring an emergency. We initiated an emergency descent flying direct to ZZZ. We were unable to maintain altitude so we ruled out the possibility of flying an instrument approach (at this time we were only 2 miles from ZZZ so we would have to fly away from the airport to fly a published instrument approach). We were still descending toward ZZZ when we keyed the UNICOM frequency to turn the PCL on high. We overflew the airport and at this time gained sight of Runway 15/33. We then turned a modified base to final onto Runway 33. Our forward visibility was obscured due to the ice that had formed on the windscreen. On 1/2 miles final; we realized that we had still not lost enough altitude during our emergency descent so we executed a mid altitude go around. The aircraft was unable to effectively climb under full power; so we maintained altitude and joined a right downwind for Runway 15. At this time we executed a successful visual approach and landed safely on Runway 15. I feel that our encounter with icing conditions was due to several contributing factors which could have easily been avoided. Our preflight preparation was not adequate given the distance of the flight. We should have obtained a complete briefing from FSS as well as obtaining a more thorough briefing from Flight Watch upon our contact. Another major factor during our flight was our hesitancy to abort the flight prior to reaching ZZZ3 when we realized that weather had moved into our area of flight earlier than anticipated. This was also due to our over-reliance on our NEXRAD system which gave us the false impression that the weather in the area was not as severe as it actually was. It is my belief that these factors combined attributed to our flight into icing conditions. Supplemental information from ACN 819212: We were roughly 15 miles from ZZZ3 when we entered an area of freezing rain. Knowing that we could not withstand freezing rain for more than few moments we made the decision to make an immediate diversion to ZZZ and requested a descent as low as possible. Center cleared us direct ZZZ and cleared us for a descent down to 3;100 FT MSL. Shortly after initiating the descent; the freezing rain subsided. We broke out of the clouds at roughly 3;300 FT MSL and let Center know we had the airport in sight and would need a change of frequency. We continued our descent to the airport keeping it in sight at all times. We broke out pretty much over the top of the airport and I set up for a downwind to Runway 34. Because I was unsure of how much ice had accumulated; I kept the airspeed high and tried to maintain a higher than usual altitude on the visual approach. Upon turning final; I lost a visual of the runway. I stated that I lost visual and my CFI replied that he still had view of the runway; however; it was very limited. The flight controls were exchanged and he continued down. Most of the windshield was covered in ice so we had very limited forward visibility and had trouble judging our distance from the runway. As we got closer; I was able to get a bit of a view out the side windows forward. Soon it became obvious that we would most likely overshoot the runway so; before losing too much altitude; we initiated a go around. My CFI held altitude and the airspeed began to bleed off. It stabilized shortly thereafter. We did not climb much during the go around; however; had enough altitude to make another attempt. He turned left at about mid-field and set up for a right downwind to Runway 15. He could see the airport out of his right window and made the best pattern he could. Once turning final he stated that he had lost sight of the runway completely. At this time I had a very limited view of the runway out my side window because of a slight crosswind. I stated that I had a limited view and that I would land it. We once again exchanged flight controls and I managed to land safely with an extremely limited view of the runway. I stopped the aircraft of the runway and my CFI had enough view out his right window to taxi safely to the ramp. he taxied off and shut down. The owner of the FBO lives on the field and let us into the building. Soon after; we spoke with Center on the telephone to verify that we had landed safely.