Maggie's Farm

Well, it's not entirely stupid. A warmer world is more humid because the vapor pressure of water rises with temperature and 70% of the Earth's surface is water. This means more precipitation everywhere (fewer, milder droughts) including the poles. The poles are always below zero, so the precipitation comes down as snow and accumulates as ice.

PS. The temperature difference between the equator and poles drives atmospheric and oceanic circulation. A warmer world has a smaller temperature difference, so atmospheric and oceanic flows become less intense. The result is fewer and milder tornadoes and hurricanes.

That said, climate is driven by the solar cycles, and carbon dioxide has only a minor supporting role. Which is why 20 years of rising CO2 has accompanied 20 years of falling temperatures.