Don't use chicken wire. It can be chewed thru really easily by predators. Use hardware cloth. Predators can smell quail for miles away. So make sure you bury something deep. I like to use railroad ties for my aviaries. I bury one to the top and then place another one on top. Nothing will dig this deep. As long as there are no air holes to the inside from the outside, they will not dig. Predators smell for moving air.
Quail can tolerate incredibly cold temps, so that is not a problem. However make sure to acclimate yours before you take them out permanently.
I use fake christmas trees for cover. The need hidey places and don't like to be exposed. But any cut branches from trees will work. I did this for the first few years, but got tired of hauling out dead branches and cutting new. So I opted for fake trees.
You can build over grass and plants, however over time they will eat these. Quail love certain types of grasses. You will have to experiment on what types yours enjoy.
Good luck with your aviary and birds! Quail love the freedom and will live far longer in aviary style environments. I have some 7 year old birds that refuse to die. LOL Just keep going and going and going. LOL