I've been waking at night very thirsty also. I think it's b/c my ceiling fan is on high and it's very dry in there. I've also had morning nosebleeds from the dryness. I know I'm well hydrated during the day, but I NEED to drink every time I wake up at night.
When your milk comes in, it is important to keep up the drinking. Dehydration can definitely lead to supply problems.