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I hang apples, cabbage, bundles of kale/mustard greens.
You can also use a suet basket and stuff it full of things like squash, cucumber or soft fruits that don't hang well.
Toss a bit of (uncooked) oatmeal, cracked corn or boss in the coop, usually it will "disappear" into the bedding and they will hunt and scratch, that will keep them busy.
I live in south east, but my bamboo is pretty much green all year, I cut branches from the tops and hang bundles of those in the run, but if you have it, you could do a small amount in the coop. They love to "hide" in the branches and they eat the leaves too.
Give them a pumpkin or spaghetti squash to work on.