I've flown MD80's for 15 years, often in winter conditions and on slippery runways.
One thing during during approach briefing is the threat analyzing. It is paramount in winter conditions or wet runways, that the issue with tail-blanking is mentioned. The only way to get back directional control is un-reverse and forward idle.
I'm not speculating that this happened here, only stating a big difference with this particular aircraft type versus Airbus and Boeing with wing mounted engines.