Before the positioning flight, the airline transport pilot monitored the weather and noticed the weather conditions were deteriorating near the time of the planned departure. The weather conditions included low visibility, freezing drizzle, and mist. In an effort to reduce the time in the deteriorating weather conditions, the pilot performed some before takeoff checks while the airplane was in the hangar. During the pilot's "haste" to preflight and take off, she inadvertently selected the wrong switch for windshield heat. While on the instrument approach to the runway in night conditions, the pilot had no forward visibility due to ice accumulation on the windshield. The pilot executed a missed approach and contacted an instructor pilot at the departure airport to confirm the location of the windshield heat switch. The pilot then activated the windshield heat switch and enough ice had melted for the pilot to conduct another approach. During the approach, the pilot increased the airspeed due to "carrying a lot of ice." On short final approach, the airplane descended below the glidepath due to the ice accumulation. Subsequently, the airplane contacted the terrain short of the runway and then "skipped" onto the runway. The airplane came to rest upright and off the runway surface. Examination of the airplane revealed substantial damage to the left wing. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.