The argument by the left is stupid.
However, the general point isn’t contradicted by snow. The point is that if your air is warmer, it can hold more moisture. If that warm air then hits a cold air mass, as the air cools, it will release it’s moisture. If the cold air mass is cold enough, that moisture will freeze before hitting the earth, and we will have a storm.
So it is true that the warmer the upper air is, the more snow we can get. A really strong storm has warmer air, more circulation, and can suck more moisture off the oceans.
Usually, if the storm is that strong, it brings so much warm air in that the temperature goes up too much, and we get rain. We are often on the snow/rain line.
This year it has been so cold that the warm air wasn’t enough, and we got snow. and more snow. I would note that the snow/rain line for Tuesday’s storm was just south of DC, so it’s not like the same weather patterns aren’t around, it’s just the snow/rain line is further south because we are colder this year.
Of course, part of why we are colder is because the west coast is warmer (or not because, maybe in the same manner that), the cold air slipped down and to the east.
It is likely that if the temperature of the earth did increase by a couple of degrees, that there could be more violent storms (although not really because the warmer air would carry additional moisture, but because the warmer it is, since “cold” is fixed at 0 degrees kelvin, the greater temperature differentials can occur, meaning more violent weather).
Heat the air and it expands. Cool the air and it contracts. Moisture content can change, but water vapor is a gas and expands and contracts with the air. What the argument ignores is that moisture only forms from vapor if it has a nucleus or catalyst. There has to be a greater nucleus or catalyst to get more moisture formed by the vapor. Otherwise it remains vapor and stays as a gas you can breath.