OK I sort of understand marshmallow toasting if you've got a barbecue running, but, in the UK anyway, this tends to be a Summerish pastime.
So why do our North American cousins include it in their Christmas songs so much? Indeed it's not as if it's anything to do with the warmer parts of the USA because videos tend to show singers wrapped up against the cold and performing in a snowscape. When did burning marshmallows become an intrinsic part of the US Christmas festivities and why?
I don't think marshmallows had been invented when the Baby Jesus was born and as far as I know the Three Kings brought Gold, Frankincense and Myrrh not marshmallows. I haven't heard that Angels or obdurate donkeys have a particular fancy for pink and white puffy sweets, although I do know a shepherd of sorts who makes barbecues from 45 gallon drums and he has a fairly sweet tooth. It's stretching a point to suggest innkeepers with no room are generally big marshmallow fans and I bet at the point of birth Mary would have told Joseph where he could stick his marshmallows.
No, it's the mystery of Christmas.