It depends on where you are. However, for the most part Mulberrys WILL lose their leaves in the winter. Some trees such as the Chinese Elm can be either deciduous or semi-evergreen, depending on the climate they are in. I don't know if this is the case with Mulberrys also, but it could be. Even if it does keep some leaves during the winter it won't be growing, which means you can deplete the tree quickly.
I have been experimenting with ways of preserving leaves for the winter. With a vacuum sealer machine I could keep leaves fresh in the fridge for up to a month, at which point they start to show signs of break down. I also tried freezing some but found the freezer can not be set too cold or else it will ruin the leaves. I have no results yet for freezing because I am still looking for the optimum freezer temp.
If nothing else you could buy silkworm chow. Just have to be ready for the bill...
Aaron