A warmer atmosphere holds more moisture until conditions cause it to rain or snow out. It could easily be the case that when it snows there will be more of it. Right now the warmer air holds about 4 percent more moisture the the old normal.
Then, as the Arctic warms we see a breakdown of the Arctic oscillation, the circular wind pattern that tends to keep Arctic winter cold in the Arctic. When the oscillation turns negative, cold air can escape into North America and Europe. During the coming few years we could see colder winter and more snow because of overall, average global warming. But we'll also see the snow line moving farther north and further up the mountain over time as things heat up more.