The pilot received a weather briefing at 1030 EST for a cross-country flight. The cross-country originated at Benton Harbor at 1100 EST using runway 27. At that time, the runway was bare and dry. The flight proceeded to Battle Creek and Kalamazoo, and then returned to Benton Harbor at about 1415 EST. Before arriving, the pilot called Benton Harbor for wind and runway conditions, but received no reply. While entering the traffic pattern, the pilot observed the wind from about 200 degrees and saw small finger-like drifts protruding out onto runway 27 for about 1/4 of its width. Runways 13/31 and 18/36 had not been plowed for 4 weeks and were closed. Considering the remaining width of runway 27 and its excellent condition at 1100 EST, the pilot elected to land even though there was a moderate-to-strong crosswind. On touchdown, glare ice was encountered on the entire width of the runway. As the aircraft slowed, the wind blew it off of the right side where it momentarily went up on its nose.