It is generally safe for pregnant women to drink cool water. In fact, staying hydrated is crucial during pregnancy as it helps support the baby's development and prevents common issues like constipation and urinary tract infections. Drinking cool water can also help alleviate some discomforts such as heartburn and swelling. However, some women may experience sensitivity to cold temperatures during pregnancy, so it's important to listen to your body and adjust accordingly. If you have any concerns or specific medical conditions, it's always best to consult with your healthcare provider for personalized advice.