The pilot received 2 weather briefings. Most of the first briefing was spent finding an alternate. The forecast included IMC with low ceilings, low visibilities with light snow, fog, and possible freezing drizzle. The aircraft was not certificated for flight in known icing conditions. During arrival, the plane entered an overcast at 3500 ft MSL. Two minutes later, the pilot reported an encounter with freezing precipitation. The first approach was abandoned in the vicinity of the FAF/outer marker after the pilot flew through the localizer course line and was about 1/2 mile to the right. He was vectored for another ILS approach. While inbound on the approach, he was informed that approach control had received a low altitude alert. He was reminded that his altitude should be 2600 ft until reaching the FAF; however, he reached only 2400 ft. His airspeed was much higher than normal while descending from the FAF. The plane struck a building and burned about 1/3 mile northeast of the end of runway 18.