Same is true of the Sahara.
But do you really want a two-mile thick ice sheet over half of North America and Europe to get a few more inches of rain elsewhere?
Or maybe, as some theorize, it is the greater precip in Winter, for whatever reason, that results in ice sheets thick enough to linger through summer?
Imagine, someone believing that so much snow can fall that it doesn’t melt all summer, due to cooling — despite the fact that without heat, the snow couldn’t condense and freeze in the first place.