The pilot was flying a GPS approach in instrument conditions with icing present. The pilot later stated the airplane broke out of the weather about 300 feet agl and 300 feet right of the runway, with as much as ¼-inch of ice on the wings. The pilot corrected but overshot the runway, landing hard in the grass. The airplane traveled about 1000 feet before re-entering the runway. Post-accident examination revealed the right wing’s rear spar was bent.