So, the drum and buckets have those little cups that fill with water but they're otherwise covered. I plan on getting submersible water heaters to keep the water from freezing.
I'd heard about the walking on snow thing before! The run will probably get snow in it, at least to an extent. It's against our garage so the back length of it is protected and we plan on wrapping a good portion of the exposed areas with tarp to block the frigid wind and snow as much as we can. Since it'll be wrapped, we're also adding a daytime light to the side of the garage, inside the run, so that they'll still a good amount of light. It'll still be cold, of course, but we're trying to make it so that they can still use the run as much as possible.