Interesting! I've never tried mulled wine, despite having lived in the UK for a while. Must try this recipe!
Swedes drink copious amount of our equivalent, "Glögg", which I suppose will be very similar to the Danish version.
A common misconception here in Sweden is that you easily "cook off" the alcohol if you accidentally let it boil. Not true at all. In fact, most of the alcohol will still be there after a short boil, so don't drink while driving.
If you're after alcohol-free versions there are several on the swedish market, but not sure how readily available in the UK. Perhaps at Ikea, but do steer clear of the vile apple-glögg they have there.