Glühwein *is* mulled wine...
My wife is German... We do
Glühwein every year. She often cheats and gets little mulling spice teabags from Germany but we've also done it from scratch... Ingredients in tea bag: Orange rind, cinnamon, cardamom ,cloves, sweet blackberry leaves.
We'll use a few tea bags (3ish? 4ish?) for 2 bottles of 3-buck Chuck cabernet from Trader Joes, plus 1/2-3/4 wine bottle full of water, 1 additional cinnamon stick, juice of 2-4 oranges, and 1 whole orange thinly sliced (skin and all)... All tossed into a pot. Heated on the stove just below a simmer. Add a bit of sugar to taste, but the OJ often has enough sweetness..
Here's one that looks similar to what we do when we run out of the teabags:
https://germangirlinamerica.com/gluhwein/This recipe adds brandy... We don't...
But we do optionally add a shot of rum to the mug (mit Schuss) if we want a bit more
Glüh (glow)
Here are tea bags
Maybe some of the HBTers in Germany can chime in, too...