Yes, too cold to snow. The amount of water vapor in the air is very temperature dependent. Even below freezing air can have water vapor: http://www.engineeringtoolbox.com/relative-humidity-air-d_687.html
So as the air cools more and more, there is less vapor available for snow.
So another side effect of the overall warming can definitely be larger snowfalls in the winter - there is more moisture in the air to work with.
You do realize the interior of Antarctica is one of the world's largest deserts, right? Because it is so cold that the air can't hold very much water. And now it is receiving large snowfalls because of the increased water vapor. Look at that chart, and see how much the % increase is from say 0F to 15F (remember, the amount of warming is much larger in the arctic areas) - nearly double.
So yeah, more heating == more snowfall.