I find it very unintuitive to think about this chemistry concept in terms of freezing, but far moreso to think about boiling.
As water heats to 100 degrees C, it boils. While it’s boiling, the temperature stays at 100 degrees C, because the energy is now being used to convert the water to steam rather than to increase its temperature. Once it’s fully converted to steam, it may continue heating up. Here’s a graph of water temperature over time that shows this – the temperature plateaus for a little while at 100 degrees C while it converts to steam: http://www.chemteam.info/Thermochem/Time-Temp-Graph-4.GIF
The same thing happens in reverse when water freezes, which means that the plants will stay at 0 degrees C for a while rather than rapidly falling to the temperature of the below-freezing air. Once frozen, the ice can drop below 0 degrees C, but the process of freezing delays this cooling.