I use the deep litter method for chickens, but don't care for it for the rabbits. Even in Alaska we get several periods each winter, and often in the fall and spring, where temperatures warm up enough to thaw things out, and thawing deep litter is a wet mess of ammonia stink if it is disturbed (for instance, scratching chickens and digging rabbits). If you raise rabbits in a big colony it probably works out, but since I breed for show I need to know who's doing what, when and with whom, so mine are in cages.
Way back when, I had some hutches with solid floors, and those were a nightmare of urine glaciers in the corners, with straw and shavings combining with the poo and pee to make literal bricks. Getting them clean was both difficult and extremely unpleasant, because much of the winter they were frozen solid so quickly that it was impossible to clean them every day (also impractical with our lifestyle). I'm pretty sure it wasn't healthy for the rabbits either; I didn't actually have any sick rabbits, but the bottoms of their feet and hindquarters were pretty sticky and yellowed. I like my rabbits clean and pretty.
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@eco2pia, I favor wire bottomed cages suspended above the ground. I don't let the chickens in there - they have their own space and I don't care for walking around in chicken poo - but I only need to do a barn clean-out once or twice a year. It doesn't get nasty, really, since there is nothing disturbing it, and it just layers itself (poo, pee, shavings, straw, dropped rabbit pellets), kind of like lasagna gardening; in fact, by the time I shovel it out, the bottom half of it is already premium gardening soil. I usually shovel in spring and fall, and I actually enjoy the work, which is made even more attractive by the fact that I shovel it all into empty feed bags and have a waiting list of people who want to buy it. (That's another reason I keep the chickens out - pure rabbit waste doesn't need to be composted, but add chicken waste and people can't just dump it on their gardens.) Barn clean-out actually keeps my hobby in the black financially during the fall slow-down when nobody's buying rabbits.
As far as water during the winter, when it starts to freeze we switch from bottles to bowls/crocks. A long time ago I had a greenhouse full of chicks and rabbits burn down due to a malfunctioning heat lamp, so I now steer clear of electric heat in my barn and just deal with frozen crocks. I try to have double the number of crocks as cages, and the plan is to give them a bowl of warm water in the morning, then switch it out with another bowl of warm water in the evening. I say "the plan" because it is the job of one of the kids, so it doesn't
always happen that way. In between times, if (when) the water in the crock freezes, the rabbits can and do lick the ice in the bowl. My daughter sometimes takes a bucket of warm water (not hot, as that can break the frozen bowls) with her to the barn, and drops the crocks into that to release the ice, then returns the bowl to the cage with warm water in it. If we have enough crocks, when I'm doing the job I just collect the ice-filled bowls in a bucket and fill other, warm ones I've brought from the house with warm water from a jug. I leave the bucket of frozen ones in the utility room to thaw for the next round of crock-swapping.
A really great trick my clever husband came up with years ago is to freeze blocks of ice in empty plastic or silicone containers, which has gone a long way to keeping the rabbits healthy and hydrated. I use yogurt or cottage cheese tubs, or my favorite, silicone bread pans, which are easier to release the ice from. I add a little bit of carrot shavings or apple cores to the container so that they freeze into the middle of the block. We pop the ice blocks out of the containers and put one in each cage, where the rabbits chew on them and play with them, trimming their teeth and getting hydrated and a little treat at the same time. We give them these ice blocks in addition to the water in the AM and PM.