Any tracks in the snow? It would have been a fairly large animal to remove them without leaving any drag or skid marks, especially if you have soft snow, like we do now. Coyote, fox, coon. As for keeping your birds safe from mink/weasel: if you could push a quarter through it, one of these could get in. 1/2" hardware cloth, well secured over all openings is needed. The predator will be back.