A BE-58 ran off the far end of the runway when braking action was nil vice fair to good as reported by a county vehicle. Later discovered the runway was solid ice covered by snow.

Narrative

AWOS reported ceiling 400 FT; braking action fair to good reported by county vehicle. When handed off to Approach I was cleared to 2;500 FT; cleared the ILS Runway 25; report cancellation in air or ground. The aircraft intercepted the glideslope outside the outer market; and I dropped approach flaps and gear; and verified three green. I reported just crossing the outer marker. I checked AWOS again which still reported same braking action. At 400 FT I broke out; had the runway in sight and canceled IFR. The Controller asked me to report braking action on the ground. I wonder what he knew that I didn't? I uncoupled the autopilot; lowered speed to 100 KTS; and came over the fence at 95 KTS; still right on the glideslope and centerline. I was concerned about the white runway; so I dropped final flaps and reduced speed to 90 KTS and set up for a flare into a full stall and landed on the centerline. I immediately felt the wheels sliding to the left; arrested the slide with a moment of differential power to get back on centerline; and touched the brakes to check traction. The aircraft slid left to the left so I released and rhythmically tapped brakes gently. Each time I braked I felt the plane sliding. It felt like solid ice. I continued tapping with no grip on each tap and thought the plane would stop by the end; but it ran past the threshold; and the front wheel got mired in deep snow and the nose gear collapsed. It was actually very gentle coming to a stop; about 30 FT from the threshold. I was not pulled hard forward and there were no marks on me from the seat belt. I shut the plane down and exited. I took pictures of the runway. There was snow on top of solid ice; with no sand.