You can go to most carpet stores and buy a piece of remnant carpeting for next to nothing, so why would you want to take some old smelly piece of carpeting out into the woods and put it into your tree stand?

There is a time to be cheap and then there is a time to spend money.

Styrofoam insulation inside of a tree stand that does not have any windows wouldn't make a big difference one way or the other.

If you want to stay warm, build a fireplace and put a Kerosun heater inside of it.