I would not.
The chicken can snuggle down with her feathers over her feet, and the wood warms up a bit, and they seem to be fine.
Also, anything thick and soft will get dirty and ripped and worn after a while.
If you have extra roosts, I suppose you could wrap some and not others, and then...
Tarp sounds good to me.
I had chickens through two different winters in the northern part of Virginia with a tarp and no insulation. The tarp covered the roof and three sides, and I made sure the "open" side (wire mesh) was facing away from the main wind.
Having just one side open meant that...