During takeoff on a snow covered runway at night, the aircraft ran off the left side of the runway and was damaged. At that time, the runway was covered with a thin layer of dry snow over the top of hard packed snow. A 50 ft strip had previously been plowed along the 150 ft wide runway. However, the tower was closed and no snow removal was permitted after 2400 CST. The pilot reported that he was concerned about the oil pressure after starting in cold weather. As he applied takeoff power, he glanced at the engine instruments, oil pressure and temperature in particular. He stated that he 'had just gone visually outside' when the copilot said 'watch yourself.' At that point, the aircraft was angling to the left. The pilot kept the nose wheel steering engaged and applied right rudder, but was unable to maintain runway alignment. He reported the left main gear was in 3 inches of snow while the right gear was in 1 inch of snow and this increased drag to the left. The pilot believed that improper snow removal was the 'sole reason.' Other aircraft landed and departed without major difficulty.