Jack, sorry I read this late.
The key to avoiding some damage is to insulate with multiple layers against moisture being retained on leaves and the cold air.
I have the heaviest frost cloth (cheap from Farmer D's) floating over top of the crops and then PVC tunnels with 6mm construction grade plastic (normally what you find on your crawlspace dirt) over top. I have PVC clamps (binder clamps work) to hold it on and rocks/boards anything to weigh down. Old shower curtains and other plastic (at least 6mm) thick work great. This needs to be away from all the plant material and above the foating later: your are creating small pocket of airspace (don't make your tent too tall!) in layers to hold in some heat. Ideally the goal is to heat the inside up and hang onto the heat for as long as possible.
How can you hang onto the heat? Well, you create heat sinks. Sometimes that is the soil itself which needs to be kept moist while the foliage is kept dry. Cold air desicates the soil, and it's better to have frozen soil than dry and not frozen...plus if it's moist it heats up way better and holds the heat & humidity in that tent for longer. Placing bricks, and rocks inside to absorb and disperse heat works well too (as do milk jugs filled with water).
The key is to be sure and vent the structure before you leave for the day if you go out. The interior of this structure is at least 20 degrees warmer than outside when the sun shines. When it is night, you are hoping to insulate everything from 5-10 degrees. My frost cloth is at least 4 degrees of warmth at all times...
I re-use my materials every year by storing stuff in plastic tubs and on "rafters" built into the crawlspace. This way they take up little room to store and keep. Each bed is about $5.00 in materials for the weather protection and all last a minimum of 3 years. Cheap when you consider the food you can get out of one bed!
