You dont need heat for chickens or ducks to lay i have never had heated coops and mine have many winters layed all winter and the temps up north here are much colder im sure then most of you are used to. There is a endless amount of reasons to why they might stop though, stress for instance doesnt take much, a change in food some of the littlest changes in environment can cause this so its near impossible for anyone to guess on what your change might have been.
Here is a thought,I read where some people mix some cayenne in with the laying mash,so I tried it,and I went from 2-3 eggs aday,to 6-7.The hens have no capsasion receptors,so its not hot to them,and it does not affect the taste of the eggs.I am totally convinced it works!!!
Have you added extra rations to help the birds compensate for the cold? Maybe a little bit of scratch grains or some leftovers? All I know is my girls are eating more feed than they did when it was warm weather. Their laying hasn't decreased much with the addition of light and scratch.