I've seen a lot of debate about this, the consensus here is that continental snow doesn't really have much bearing on Arctic sea-ice. Recently (2017, 2018) the snow mass charts have gone off the scale in winter (ECCC had to make a new y-axis) and it really hasn't correlated with a change in Arctic sea ice melt.
More snow = more sunlight reflected = cooling. But the best way to get a wider cover of snow on the continents adjacent to the Arctic is to disrupt the polar vortex and allow more cold arctic air to spread further away from the central Arctic, meaning the central Arctic becomes warmer.
Yes! Extra snowcover also has the impact of aiding -500MB anomalies in the continents, with ensuing cold blasts into the mid-latitude oceans a particularly potent method of advecting additional oceanic heat into the Arctic. Continental snowfall is good from the perspective of blunting incoming warmth to the Arctic that would originate from the continents, it is bad from the perspective that -500MB anomalies are effective at evacuating mid-latitude oceanic heat northwards, into the Arctic.
IF the continents are snowcovered AND the Arcic is fully ice-covered, the outcome of snow-covered continents is probably net beneficial to sea ice. However, if the continents are snowcovered and the Arctic pack is entirely surrounded by water -- as is currently the case -- perhaps this is when the oceanic feedbacks derivative of the -500MB anomalies really kick into overdrive. When the sea ice is surrounded by hundreds or thousands of miles of open water, the positive benefits of continental snowcover are lost as that air which would normally advect overtop the sea ice, depleted of heat and moisture, is instead often muddled by cyclonic activity as it meets the open waters of the ESS / Laptev/ whathaveyou.
I had not considered this juxtaposition before, but it would make quite a bit of sense in explaining why atmospheric circulation goes to particular sh*t in the autumnal months as of late.
