Hey - you can - look what I found
50 to 100 pounds of dry ice dropped directly into a heated swimming pool will make fog for an hour or longer depending on the water temperature and the size of the dry ice pieces. Because of the Jacuzzi's hot water, it makes the most fog the quickest. As long as the water is kept hot, it can take 50 to 100 pounds per hour. The dry ice will carbonate the water for several days. If possible drain the Jacuzzi. The swimming pool will read more alkaline during this time so wait to add acid until the carbonation has dissipated. If the temperature of the water in a swimming pool, fountain, waterfall, or birdbath is too cold (less than 60°F) the dry ice will bubble but produce much less fog.
Of course - unfortunately, we don't have a heated swimming pool. And in October, the temperature of the water is going to be about 65. Might have to find some kind of floating container myself.
P.S. It's my DD's 11th birthday too that we'll be celebrating!