Drinking your cold water is fine. And no, it doesn't defeat the purpose of the exercise.
The purpose of the exercises (and the heat), according to Bikram Yoga is :
Yoga changes the construction of the body from the inside out, from bones to skin and from fingertips to toes. So before you change it, you have to heat it up to soften it, because a warm body is a flexible body. Then you can reshape the body any way you want.
Hatha Yoga flushes away the waste products, the toxins of all the glands and organs of your body. It provides a natural irrigation of the body through the circulatory system, with the help of the respiratory system. It brings nourishments to every cell of your body so that each one can perform its function and keep your body healthy. Bikram Yoga also employs heat to further that cleaning process: When you sweat, impurities are flushed out of the body through the skin.
However, with such exercises in the heated room and for that duration, you're bound to feel dehydrated. Without the water, you might not be able to perform optimally and your exercises might be in vain.
Obviously, you want to drink as infrequently as possible while maintaining your hydration. But drinking the cold water seems necessary.
So yes, listen to your body and respond appropriately.