Carefully peel the zest very thinly from the orange and lemons using a vegetable peeler. Squeeze out the juice and reserve.
Stick the cloves into the satsumas.
Pour the wine, 1.2 litres/2 pints of cold water, and the citrus peel and juices into a large, heavy-based saucepan. Add the clove-studded satsumas and cinnamon sticks. Bring the mixture just to the boil, then reduce the heat until the mixture is simmering, cover the pan with the lid, and continue to simmer for about 1 hour. Stir in the sugar gradually during cooking, until the mulled wine is sweetened to your liking (you may not need all of the sugar).
Strain the mulled wine and serve hot in cups.