Air can hold water vapor , this is measured as humidity. Warm air can hold more water than cool air. As air cools, a point is reached where the air cannot hold any more water, and if it cools more, some of the water condenses out of the air and becomes liquid water. This is the dew point. The liquid water that collects on cool objects in the area is dew. The dew point (temperature) can be different depending on what the relative humidity of the air was. This has nothing to do with frost nor freezing.
By definition this is the temperature where liquid water turns to solid water, that is ICE. Frost = ice.
It is 32 degrees F where this happens. You cannot have frost unless the temperature gets that cold. Absolutely impossible.
So your plants got blackened? It sounds like they got frozen. To freeze the temperature at the level of the plants had to be 32Â° F or lower. That is just a simple law of physics.
Sorry you got hit. The potatoes will recover. I am surprised the peas took a hit. They usually have pretty good resistance.
A cover like a blanket is better than a bucket or jar as it has better insulating qualities.
It is good to wet things down well if expecting a frost. Water is interesting in that it must give off quite a little heat even after reaching 32Â° before it will change state (freeze). So more water = more heat.
It soon becomes obvious that there are cold pockets and six thermometers in six locations will all read different. Best to expect frost any time the forecast is for under 40Â°.