If the temp dipped below freezing last night and the humidity inside the tarp was high then the interior frost could have resulted from tiny frozen water droplets which condensed on the inside of the tarp. Apparently the ground temp wasn't warm enough to keep the "tent" temp above freezing. Hope you plants survived ok.

If the tarp was plastic, that was the mistake. I also hope your plants are okay. I haeve four pots of Virginia Bluebells that I didn't get in the ground yet-the other five, I already planted, but then I got sick and have not been out all week. Good luck to us both!

That's entirely understandable. The tarps got cold, because they were touching, and exposed to the frigid outside air. That doesn't mean the air temperature under the tarps was below freezing, and it's that air temperature that plants are affected by. The tarps did provide insulation, so I'd have to assume that air temperature under them was well above that of the outside air. If the temperature under the tarps got below freezing, you'd be getting frost forming ON THE PLANTS themselves.

Plastic should work fine. The function of the tarp is to prevent warm air coming off the ground from escaping. You want to seal in that warm air. Plastic will do that handily (as would steel and ceramic, if you could make a tarp out of those).