While this advice is possibly less helpful for campers, can I suggest that when sleeping indoors in cold weather, find a second hammock, ideally one that's stretched, and hang it from the same hooks, then sandwich any insulation you choose in between the two hammocks. You can then sleep on the upper hammock normally.

My chosen insulation is either an old doona folded in half, or 3 sheepskins.

If your 2nd hammock isn't sufficiently stretched, add a short length of chain or rope to hang it an inch lower than the main hammock.