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If there was more snow in 2012, I'd suspect that may result in more insulation of the ice over winter, making it harder for the ice to thicken, and resulting in a thinner ice sheet during 2012. The thickness of 1st year ice at the end of winter is strongly influenced by a thermodynamic balance between heat escaping from the ocean below, and the cooling effect of the very cold air above. Once the insulation from the thickening ice sheet grows high enough that the two are balanced no more thickening occurs. Snow provides more insulation per litre of frozen water due to the air trapped in it. The other factor is that higher amounts of snow will fall when temperature are close to freezing, which is poor conditions for ice thickening. When temperatures are very cold the atmosphere cannot hold much moisture and less snow will fall.
Excellent paragraph! I feel the thing about "less snow when air is much colder than 0C" is not that simple, though. I know that there are certain cloud types which are not moisture, but ice (microscopic ice particles). Obviously those are not affected by how much moisture athmosphere can hold (directly). But IIRC, the process of actual snowflake formation is very much related to relative humidity, and as temperature drops, that changes. And another, probably much more important, thing - late autumn/winter, i think the cause is not "how cold athmosphere is", rather, it's "how much moisutre there is in the athmosphere". If lots of clouds come in (from anywhere else to a given region), that's lots of moisture alright, and one of major effects of it - is massive reduction of the loss of heat content of the athmosphere. I mean, clean skies (little/no moisture) -> surface and athmosphere radiate lots of heat out into ~3K near-Earth space, and things get real cold fast; but when it's lots of moisture, much of that radiation "stays" within the athmosphere.
I.e. the dropping temperature gradient between Arctic and moderate zone, most roughly speaking, should allow for more mixing - more Arctic air going much south and in return, more warm air going into Arctic, which means more moisture into the Arctic, which means slower cooling of the athmosphere late autumn/winter and, of course, more snow - and that like you said leads to slower /less ice thickening. Again, this all is extremely gross oversimplification, of course.