You may have already considered this, but plenty of other people make a square or rectangular wood frame for the door, and use wire mesh to cover the rest of the end.
Tarp is one option for weatherproofing, but it needs to be fastened down tightly so it cannot flap and shred itself, and replaced regularly. In my area, cheap tarp will last all winter, more expensive tarp will last at least two full years. The times I've used it, my structure was heavy enough or anchored well enough that it didn't blow away, but I can't predict what would happen in your conditions.
A few articles with photos:
https://www.backyardchickens.com/articles/the-hoop-coop.65569/
https://www.backyardchickens.com/articles/aarts-hoop-coop-chicken-tractor.72211/
https://www.backyardchickens.com/articles/mos-cattle-panel-hoop-coops.73385/
https://www.backyardchickens.com/articles/cattle-panel-hoop-coop.74636/
(I just looked at the photo at the top of each article, rather than reading all the details for how they constructed it-- the construction looks fairly obvious to me, and I doubt you would be exactly following anyone's directions.)