I think the most frost protection comes from solid clear plastic film, not the non-woven breathable products.
But plastic may tend to blow away even more than than the more. I guess that keeping it low helps. Maybe lay 2x4s or bricks and shovel dirt on top of the edges for extra weight.
Hoops: metal conduit is not much more expensive than PVC pipes. I think the width of the beds determines how strong it has to be. There are 1/2" and 3/4" versions
I think that thin-wall electrical conduit called EMT (Electrical Metallic Tubing) is the cheapest rigid material. You can bend it and then it holds its shape.
With PVC, you bend it and stick it into the ground under tension to keep it bowed. I have read that the plasticizers in PVC pipe weakens plastic film over months or years, but I don't know, myself.
I seldom see hoop tunnels with horizontal cross pieces lashed into place, but it seems to me that they would add stiffness to a tunnel. But probably the problem is more like "the plastic blew away" that "the whole tunnel fell down".
I hope someone with
experience says more!
I only made one tiny tunnel to hold a few potted plants. I tied together two lengths of welded steel fencing (wire fencing with no added ribs) to get a little rigidity, but it would not have supported 2" of snow.