OK lets not confuse a compost pile for a chicken coop. They serve two different purposes. A compost pile needs a higher moisture level to work well, a chicken coop needs a much lower moisture level or you will run into things like ammonia and frost bite. I don't think aart puts that water in...
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With the metal garden cart being off the ground I don't think the biomass will keep going through the cold winter. Too much heat loss for too little mass. So yes I think you will just have to change the littter more often then a true deep litter. A deep litter should work on...