When you get half year polar night with temperatures deep bellow the freezing point, it is quite logical that the ice will form, not depending how much was there during the summer minimum. Or the tipping pointers suggest it will once melt and never form again?
7,000 years ago, there were probably Arctic summers without any ice at all.
http://www.sciencedaily.com/releases/2008/10/081020095850.htm
We have still millions km2 of ice during the summers.
I think the ice/snow albedo feedback in present conditions is too much overrated. Maybe if you go over some serious tipping point like with Milankovich cycles and Earth slips to or from serious ice age.. but here, even half meter of snow does not slow the spring coming, all what is needed is few days of mild south-west circulation.