The ice has energy, otherwise it would be at absolute zero (-273 degrees C). It feels colder because it has less energy than the drink. Leave any two objects, at different temperatures, together in the same box and the resulting temp will be a blend of the two. The ice cools the drink and the drink melts the ice.
For example, according to ChatGPT 100g of ice at zero degrees PLUS 1000g of water at 20 degrees gives you 1100 grams at 19 degrees.
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