I am trying to deal with this exact same problem here. My doe has 11 day old kits and drinks a lot to meet nursing demands.
I've been trying to swap out with fresh warm water bottles, but the metal tube freezes within minutes so they can't actually drink the water
Do you think bowls of water are better for winter months? Will the rabbits typically adapt to something new like that easily?
I use tin cans in the winter easy to replace the frozen ones