I float my ice cream with Diet Pepsi. I'm always excited for when the ice cream gets crispy. It gets crispier when I use cold soda instead of room temperature. Is my soda freezing in the ice cream?
I think I know what you mean, but is the ice cream "crispy" only on the surface? Unless your ice cream becomes crispy in its interior as well, (which I could not explain), I think it's simply as you speculate, the water in the soda is freezing into a crust of ice around the surface of the ice cream ball. This would explain why it is more noticeable when the soda is cold.
Turns out that my soda is freezing.
I ran a rudimentary experiment with white ice cream and dark soda. Here's a picture showing the soda freezing inside of the ice cream.
The soda on the outside is warmer than the ice cream when poured over it. This melts some ice cream and dilutes the soda with sweet creamy goodness. Sometimes the ice cream will be cold enough to freeze parts of the soda onto the ice cream causing this "crispy" shell that I like.