You can definetly keep zebras outdoors. I kept my cordon bleu caps, owls, strawberries,parrot finches and more outside in my aviary. Yours aviary sounds more sheltered than mine. I have a flat roof but I did wrap the whole thing in heavy greenhouse plastic. When it got to freezing at night I'd sometimes turn on a heat lamp.
I plan on the same thing this year but am hoping to get a gable roof on one end of aviary so they canget up under the shelter.