Dry ice is interesting stuff, and it has practical uses of which I was unaware, until I seized on it as a name for this cocktail. About all I know about it is that when you put a "soft" object into it--like a rose, for instance--it turns it brittle as glass! The gassing off appears as a "smoky" or simmering cloud, as if it were hot. But it's very, very cold! At atmospheric pressures (on earth) it is -109.3 degrees Fahrenheit! That's cold. You have to handle it with care, since if it touches you it can cause "freeze burns" of frost-bite. That's what happens to people who climb mountains in the Himalayas! Ouch!
But more to the point, tropical drinks are designed to cool you down. It's true that alcohol actually has the opposite effect when ingested. But in the eye of the overheated customer, a cool drink with lime overtones has an irresistible attraction. Which is why so many citrus cocktail drinks are consumed during the hot summer months.
Crystal structure of dry ice
So here's my version of a rather dry, but seductive Summer lime flavored cocktail, measured out, as usual, by proportion, rather than as a total (don't want to encourage an unnecessary inebriation!).
4 parts white rum
1 part cachaca
1 part créme de bananae
1 part limoncello
juice of 1 1/2 whole fresh lime
--shaken vigorously and served up in a chilled cocktail glass.
I guarantee this will make you think of the Bahamas, or of Mazatlan, or of the Cook Islands. Or perhaps of British India during the height of the Raj. We all have our orient of the imagination.