This doesn't make sense to me. Wouldn't the answer be "她要冰水吗?" since Chinese doesn't really have a parallel to these kinds of conditional statements in English?
I follow your mindset, but I think an 'ordinary' question would be "does he want iced water?".
When you start with "don't", it usually implies you have pre-existing knowledge that the person refused the water.
Hope it helps.
"Doesn't he want ice water?" implies that he would want ice water or that you can't believe that he would not want ice water. I suggest "Does he not want ice water?". It doesn't sound as natural in English, but it implies that you are confirming that he indeed does not want ice water.