I've seen emmies kept outdoors in FL that didn't look good to me. Then again they were imports and I don't know how long they have been outdoors. I think it could be done but believe it or not you will need to mist the animals down more then you think. A screen cage isn't going to hold any humidity. Good luck if you give it a try.

Thought I'd add IMO they animals I've seen kept outdoors just don't look near as nice as the ones kept inside, they just appear dry and dull to me.
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John Light