Personally I would not advocate the use of carpet or duvets. Even if they are well covered over, they will still get damp from dew and moisture in the air, in which case they will do the exact opposite of insulating and will draw heat out of the hutch. You also need to be very careful about covering the front of the hutch, there is a very fine line between making it cosy, and not allowing air to circulate, which can result in pneumonia as stale air and bacteria build up - I remember a tragic case on here a couple of years back where someone had covered the front of the hutches with duvets to keep them warm and one of the bunnies had died probably as a result of this.
Personally I would find some way of covering over most of the mesh with a clear plastic/Perspex etc to keep out rain and wind, leaving gaps for ventilation (easier if the hutch is over a run as the hole into the run provides some ventilation) and just ensure that there is a cosy area which is completely packed with straw/hay for the bunnies to retreat into to get cosy. One of my hutches has one of those Trixie run shelters in it, the other had a pet carrier, both stuffed with hay so that the buns can snuggle deep inside.
If you want to insulate the hutch fully, I would either insulate the inside of the walls and ceiling then cover it with a thin layer of ply to stop bunny teeth, or use a product which does not absorb water - like one of those silver insulation jacket thingies or bubble wrap, on the outside.
As aliduncan says though, you'll most likely find that they ignore it for most of the time and sit somewhere cold :lol: as they grow thick winter coats I don't find that they are generally that bothered by winter outdoors apart from those very few days each year when it can get bitterly cold.