I am not advocating a bedroll as better than a modern sleeping bag. It works if that is what you have. Wool does absorb water, though not as quickly as cotton, and unlike cotton, it will retain its insulating capabilities to a great extent even though wet. Wool is also fire retardant, and I have tested this many times as a demonstration for my scouts and their families; I would say that 100% wool is almost fire proof. I have burned cotton, and the synthetic fleece and other synthetic materials go up very quickly, melt to the body and continue to burn (I have witnessed this first hand in a parachuting accident where someone landed in power lines).
When I first joined the Army we had a cotton sleeping bag, with a cotton cover, with some poor synthetic insulation inside, sometimes you could get a down bag, but these were rare and in poor condition. The bag was bulky and would not keep you warm when wet (made by the lowest bidder!). The bedroll I described was a better solution in many ways, snd worked better in most conditions. It also had the advantage of being there when you needed it, unlike the bulky and difficult to pack sleeping bag.
Today's sleeping bag technologies are far superior than older bags in insulating ability and compressibility. I would only advocate someone sleeping out in very cold weather with a bedroll as a valuable experience to help you understand the capabilities and limitations of such gear. If you are like me and generally carry blankets in the car instead of sleeping bags, it would be helpful to understand the limitations and the best configurations of what you have. Testing is always good.
I actually have an old Russian greatcoat that I have used in the woods, and it was very warm, though it is a rough wool that itches terribly. You don't want it on your bare skin.