And what, the snow melt would run down the stick into the canteen? Or would one get the snow to slush a bit and the squeeze it into the canteen?

The only difficulty I see with the Finnish Marshmallow is that it would be hard (I would think) to keep the snow ball on the stick. As it melts, it would slough off into the fire, would it not? Or is there a trick to it? Have you actually tried it and made it work? Might be a really good survival technique.