Prepare the fruit. Cut orange into quarters and push the pointed end of a clove into the skin of each wedge. Cut each apple into 8 wedges for a total of 16.
Fill the slow cooker. In a medium bowl combine the brown and granulated sugar, set aside. Add to the slow cooker the orange wedges, apple wedges, wine, rum, cinnamon sticks and ginger. Cook without simmering or boiling until a sip reveals the flavor of the apple and cinnamon, about 1 hour. Add half of the sugar mixture, and taste. Adjust with more of the sugar blend, not every wine has the same sweetness, so tasting here is important. Stir until the sugar dissolves. Use a slotted spoon to remove and discard all of the solids from the slow cooker except for the cinnamon sticks. (Dont be tempted to press them through a strainer to get the most liquid. Pressing will make your glhwein cloudy. Then again, if you dont mind and want to salvage 1/4 cup of liquid, go right ahead.)
Garnish and serve. Place apple slices in a bowl and add lemon or orange juice. Toss gently to coat, then place a slice in each serving glass. Pour over glhwein and serve warm.