In that case, make the pen as big as possible or portable, or you will have them in a mud pit pretty quickly.
I would not give them dog food. Geese do not need the animal by-products that dog food has, or all that corn either. I still don't understand why people think dogs should eat that much corn.
Most geese are not tropical, so they are built to make it through winter pretty easily with just additional grains, grassy hay and whatever vegetables you find they like. Mine are particularly fond of turnip greens and carrots, both of which I keep in the garden all year. Its amazing how the greens survive even under snow. If you can utilize some of that acreage to start them little food plots, you'll be in good shape.