First, let me state that SWA does have an outstanding safety record. This is not a slam of an airline. None of us are perfect, and I know for a fact that I make mistakes everytime I fly.
I don't know the feasibility of changing RWYs at MDW, I've never even landed there and I am unfamiliar with the approaches, but here is a question for those who are familiar with airport operations at MDW. The preliminary NTSB report states that had the aircraft landed with a headwind as opposed to a tailwind, stopping distance would have been 1,000' shorter. Why land on a less favorable runway under these terrible conditions? Why not ask to change runways?
This is from the Preliminary report:
Preliminary calculations show that the airplane touched down with about 4,500 feet of remaining runway and was on the runway for about 29 seconds. Preliminary calculations also show that, for the runway conditions and use of brakes and thrust reverser that occurred, the stopping distance without hitting obstructions would have been about 5,300 feet (the actual stopping distance was about 5,000 feet). In addition, had the airplane landing into the wind, rather than with a tail wind, the stopping distance for a landing would have been about 1,000 feet less.
Approximately 20 minutes prior to the accident, the winds were from 100 degrees at 11 knots, visibility was 1/2 mile in moderate snow and freezing fog, the ceiling was broken at 400 feet, and overcast at 1400 feet, temperature -3C, dew point -5C, altimeter setting 30.06 in. Hg. Remarks - runway 31C rvr (runway visual range) 4500 feet, snow increment - 1 inch of new show in the last hour, 10 inches on the ground.