See if this helps. I'm not sure if you mean ice cream or shaved ice (like a snow cone) but I believe the link above is referring to Ralph's ice cream.
Generally I've found ice cream to be around 20g Carbs per 1/2 cup serving (unless it has a lot of candy/cookies/fudge ripples, etc. in which case you should count for more carbs). And italian ice generally is around 15g per 1/2 cup serving. Just make sure that you multiply because I doubt they'll serve you 1/2 cup of anything--- it's more likely to be about 2 cups in a "serving".
If you're served the stuff in a styrofoam cup, you can also stick a kitchen scale in your purse and weigh Hana's treat. The styrofoam won't weigh much at all so you'll get an accurate weight of the ice cream/italian ice. Then you can refer to CalorieKing's weight to find the carbs.