Here are pictures of my brother-in-law's door insulation. The door itself is wooden, nothing fancy. This is the view from outside, inside was identical.
The insulation is a piece of fake leather (I think?) with a thin layer of some kind of sponge/foam insulation on one side (No pics of that, sorry). This covers the whole house side of the door, wraping around the edges.
It creates a layer of air between it and the door, which insulates not only thermally, but also acustically. I forgot to ask the price, but it shouldn't be too expensive. Brother-in-law is very happy with it, says that it's much warmer in his unheated entry room, plus it's so much quieter.