I do a deep bedding too--add a thin layer of shavings a couple times a week. In the super frigid cold, though, I put old hay in there, to give them something to nestle into, though they do end up flattening it eventually (and yes, pooping on it).
It's just a 100 gallon stock tank with a heater in it. During the summer, I drain it and refill it about twice a week, because it gets so filthy. It's above our vegetable garden, so with a 100 foot hose, I can syphon it into the garden. But it's been clear for a month now.
We've had a heater in the duck tank for the last two winters. Their first winter, they bathed down to about 10F (crazy, I know), but this winter they haven't gotten into it at ALL. No idea what's different this winter. They seem to be more sensitive to the cold, staying inside on truly frigid...