Why would wrapping a block of ice cream in paper won't melt the ice cream?

The newspaper helps keep the heat away from the ice cream. When you put a blanket over yourself, your body supplies the heat, not the blanket. The blanket simply traps the heat next to you. Similarly, covering a block of ice in think blankets traps in the cold (more correctly it blocks the heat) and the ice last longer (not forever) With thick newspaper around ice cream the same thing hold true. Paper is a pretty food insulator. Many homeless persons keep warm by lining their coats with layers of paper. You can try this at home by lining your body with newspapers before putting on your snuggie.