I think that this sort of accident is fairly inevitable when many aeroplanes around the world are landing at restrictive airports in these kind of conditions.
There are too many variables involved in the actual line operation to be able to accurately predict stopping distances. You can work backwards from whatever happened to write the accident report and do it in great detail but it's very 'fuzzy' looking the other way.
There are many assumptions made when calculating landing performance but more importantly, the actual 'input' in the 'real world' is much more variable than, say, when taking off. If you had the same crew and aeroplane do a series of takeoffs and landings, using exactly the same technique each time, I would take a large wager that they would leave the ground in pretty much the same place each time but there would be far more 'scatter' in where they finally came to rest. I feel you would observe this effect on a dry runway in calm conditions, let alone in the middle of a snowstorm.
I think that it has become a matter of 'garbage in - garbage out' in some ways. If the wind and contamination state are not what you thought they were, you carry a few more knots over the threshold, float a bit, delay the reversers slightly, etc. these factors will soon erode all of your safety margin as they multiply up. If one of these things is causing the problem on it's own, it will be more obvious but a subtle combination of slightly exceeding a large amount of parameters will put you off the end just as surely.
My final point is that if you plotted calculated stopping distances against achieved stopping distances for a significant sample of flights, you would mostly likely end up with something approaching a 'normal distribution'. Once you have established that, it's only a matter of probability that someone will go off the end of a short, contaminated runway. It's the area under the tail of the curve, beyond the overrun point, that matters and that could be significant on the runway mentioned above.
I remember landing into ABZ (pretty comparable to Midway) one snowy night in a 737. We had done the calculations (using very conservative data), the runway friction had just been measured (we took a bit off to be on the safe side) and the wind was on the nose (we used nil). With full braking and max. reverse off a fairly firm touchdown, 'on the numbers', we eventually came to a halt 50m from the other end of the runway. Not an experience I wish to repeat.