A few of my BT's refuse cold water in the depth of winter, and if offered will prefer warm in summer too. Mine only get warm water if the bucket freeze solid, and it works. I am not sure it makes them produce more milk, and if it does, wouldn't the milk just be waterier and have reduced butterfat?
Problem is if they come as older animals with certain habits... one of my GG's refuses to eat dairy nuts, in her previous place she was on goat mix... so off I totter and buy the expensive stuff...