I like the idea, but like you said, yeah it gets pretty cold like -40F, I think i'll just make sure to prevent the fire from starting as best I can, like what blackdog said by putting a wire frame at the bottom of the bucket and fully securing the heat lamp (If we choose to use one again) But I do want to use a heat lamp just to make sure that they can't get any more frostbite.
Same tactics same results I say.
Good luck
Gary