One thing that I've found to really keep rabbits well-hydrated in the winter is to give them, in addition to bowls of warm water once or twice a day, an ice block to chew on. It really seems to help the rabbits stay in good condition. We freeze water in old yogurt/cottage cheese tubs, often adding a little bit of something tempting like apple cores, carrot shavings, or sweet potato peelings frozen into the middle. We leave these blocks in the cages all the time, and the rabbits love to play with them and chew on them - they get hydrated, entertained, and good tooth-trimming round-the-clock. The rabbits love them.
Years ago, due to a miscommunication with a housesitter, our rabbits lived for a week with
only the ice blocks. I wouldn't do it on purpose, but when we got home, they were none the worse for wear.
Some have expressed concern that like humans, rabbits might get cold from eating snow and/or ice. But unlike humans, rabbits are totally cold-adapted. In fact, our rabbits suffer far more from heat than they ever do from cold. Wild and feral rabbits live on ice and snow for many months of the year in our area. There is no liquid water anywhere when it's below zero, in the single digits, or in the low teens (Fahrenheit), but they don't seem to have any difficulty. We do give our rabbits liquid water at least once a day, but I like the ice blocks because they ensure there's a source of water in case the liquid isn't available for one reason or another (e.g. dumped, drunk, fouled or frozen almost immediately when it's
really cold). Actually, my rabbits' favorite is snow - they
love that, and strangely (to me, anyway), they will sometimes eat snow before they even drink warm water. But it doesn't last like an ice block because they play with it/in it as well as eat it.
