The cheap answer is "yes" -- see custard ice creams as an example.

Typically though, "cooking" requires heat, and most non-custard ice creams wouldn't be cooked. Even in the same phrase when talking about cooking other things, you'd say something like "I'm cooking steak and also making ice cream."

I'm sure some regions use the word differently, and adding a bit of ambiguous context might make on-the-fence regions more likely to use "cook" for cold-prepared dishes. E.g., if you talk about cooking dinner or cooking a meal and then list the things being prepared (one of which is ice cream), the verb "cook" is, in some sense, being applied to the ice cream. That ambiguity can color the verbs you subsequently choose when referring to just the ice cream.

oh cool to know always learning something new about English in my country we don't have ice cream but we have words that loosely translate to make or cook food but none of them feel ergnomic with ice cream

> does one cook ice cream?

Yes. Many recipes require heating of the ingredients.

Here is one example picked randomly: https://www.bbcgoodfood.com/recipes/ultimate-vanilla-ice-cre...

"Step 4: Return the pan to a low heat and cook, stirring all the time with a wooden spoon, for 8-10 minutes, until the custard is thick enough to coat the back of the spoon."

Yes, you typically cook the custard before freezing it.

You can also make ice cream what's called "Philadelphia-Style" which doesn't have eggs and requires no cooking before churning/freezing.

But the custard method is more typical.