I use a suet cage too, but I've attached it to the run's hardware cloth walls. I never thought to let it swing. Good idea. Winter toys are going to be tough - no tomato branches to throw in, no vegetable garden overflow... Is it spring yet?
My girls live in a 5 x 12 run, and it is hard to think up things to keep them occupied. I would let them free-range if I weren't worried about some loose dogs in the neighborhood. Anyway, each morning before work, I dig up a huge clump of tall grass (our yard is left "natural", it's not a...