Have you tried them on scratch? Preferably one with several grains rather than just corn.

Geese can be picky. Mine won't touch corn, tolerate scratch some of the time and most of the time will only eat the organic layer mash I buy for the chickens.

Grazing is best for geese, of course, but in winter the turf just isn't enough. This is my second winter with geese and I worry too.

Just posted about rehydrating alfalfa hay for them. I find they eat grains better too when I soak them.

As far as the cold... they can take quite a bit, but it is good if they have a place they can get to that is out of the wind. I always put mine in their house at night and on a handful of really severe days keep them in completely. They hate it, but there isn't much out there for them anyway and MOMMA KNOWS BEST.

If your geese are the kind with the knob on their bills, please note that they can get frostbitten there and that it can be serious. I am not familiar with the Chinese/African/Egyptian type of geese... I like the "goosely geese" descended from the European graylag. I have three Pilgrims and an American Buff. So I can't be more specific about the frostbite question.

You'll find a good discussion of geese and winter feed in this old thread.

Here is a link that might be useful: Geese - Winter feeding