As a breastfeeding mother, you can pretty much eat anything you want. If you have an overall healthy, well-balanced diet, then you don't have to stop eating any of the foods you enjoy just because you're breastfeeding.
Even if you eat ice cream your breast milk will be as of your body temperature it won’t become cold or cause any harm to your baby.
Next Steps
But, why you should avoid ice cream is because extremely cold food can congests your throat, which makes it easy breeding source for infections, as your closer to your baby, your baby may get infected from you.