Carpet Padding is not the best insulator by itself but when the carpet padding is added below the carpet and the carpet on top of the carpet padding it becomes a better insulator at keeping the cold air out and the heat or air conditioning inside your home.
Carpet is nice because it keeps your feet warm in the winter and it feels much better to walk barefoot on carpet than it does on hardwood floors.
I have carpet in my living room and bedrooms and hardwood floors in my dining room and kitchen and bathroom but I love walking on the carpet barefoot much better than the hardwood floors.
I have used old carpet padding as insulation in a dogs house and inside my shed outside to help keep some heat inside when I'm working inside the shed in the winter.
What I did was add the carpet padding and old carpet inside the walls to recycle it and it made a pretty good insulation when added together.
The shed stays pretty warm with my propane heater inside but I don't spend a whole lot of time out in the shed but when I do the heat is nice and the carpet padding and old carpet made good recycled insulation.