Place the mince, mushrooms, chives and wine into a large bowl. Stir the mixture so that it all combines.
Place the wrappers on a flat surface. Spoon 2 teaspoons of the mince mixture onto the centre of each wrapper. Brush the edges with cold water. Fold up the sides to form a square pouch. Pinch edges together to enclose. Place on a tray lined with baking paper.
Place a steamer lined with baking paper over simmering water. Cook the dumplings in separate batches, for 15 minutes or until tender and cooked through.