I made a mat for my DGD when she was a baby. Instead of cotton backing I used Rip-Stop, similar to what spray jackets are made from. It doesn't make it waterproof but it's water resistant.
My daughter loved it for taking to the park. All her friends asked where she got it. I did a quilt for a friend's GS recently and put Rip-Stop on the back. I used polyester batting for the loft in both cases.
Rip-Stop is made of nylon.