I would just buy a small package of vine netting and attach it with something like zip ties or fishing line. Eventually it can be removed. Minimal investment both in terms of time and money.

Thanks, mbevac. I just looked up vine netting on Amazon and that would be perfect. But there's no reason chicken wire wouldn't work also, is there? I have a lot of it on hand. I guess the downside is that it would be more visible than the vine netting.

Chicken wire would work fine. Even fishing line would work (which is what a lot of cheap netting basically is - a type of nylon string).

The issue with anything running only horizontally is the ability to keep it in place. You can run a bit to the top, tie it off, pull it really tight...any number of things, really. For an idea on a homemade trellis, the following video is fantastic (because it's so easy): https://www.youtube.com/watch?v=JAMqZA27iA0. I used his method with paracord and it worked wonderfully. A modified version would be perfect for your area because you already have the "top" in place, so you can just run wire down and then across (likely you would wrap the wire, not tie it off in the way he did). But, the video is one of many ways to accomplish your goal. Be creative because it's only a temporary solution. If you botch it, you can rest comfortably knowing it's only there a couple months.

One note which is probably obvious, but, if you plan to do any restoration make sure to do that first. I can only imagine the headache after it is covered in vines haha.