"Warm" is relative. -40 degree air can probably hold more water than -50 degree air. Warm air over water can evaporate more of the water, which can be carried to cold places.

Also, as a comment (iirc) on the Ars Technica take on thus story pointed out, the error bars on the study are so huge that it's unreasonable to conclude the ice is thickening without more accurate data.

Precipitation doesn't fall where it enters into solution with the atmosphere.