Have you ever tried this conductive ink before? You can buy a few from the range online at Mindsets and also at Bare Conductive themselves and they are fantastic. We used some a few years ago just before Christmas as a fun session for our STEM group and we have just ordered some Christmas Card packs for our current STEM group.
I think, first of all you colour in the card/design (because they do little houses that you can build, too) and then you make the circuit. Although it was a few years ago that I did it so it might be the other way around. In most of the kits, for every 3 cards you get a conductive ink pen, which you can also buy separately, and you use this pen to draw the circuit. Then you might have an LED or two to put into the circuit and the battery. When you connect up all of the circuit, the LED lights up.
What a novel Christmas card that you can make! Hopefully our order will come in time for the last session of the year and everyone can make their own, personalised, light up card!