As we descended, the temperature descended with us. At 5,000 feet the thermometer showed 29 degrees and, still in the clouds, our ice overcoat was continuing to accumulate. We were as low as we could descend over the mountains of Kentucky, and I made the (wrong) decision to climb out of the clouds. Back up through the overcast we climbed, with ice continuing to accumulate. Sure that we would soon break out of the clouds and the accumulation would stop, I held the controls as steady as I could, and we maintained a climb rate of close to 200 fpm through 7,000 feet. We were cleared to 11,000 feet. Steady on the stick. I eased the airplane through 8,000 and then 9,000, clawing my way upward at 100 feet per minute, and broke out of the overcast at 9,400 feet.