How it works:
To take liquid water and freeze it, two things have to happen:
- The water has to be cooled down from its initial temperature to 0 °C.
- The water has to undergo a phase change from liquid water at 0 °C to ice at 0 °C.
To cool the water down from its initial temperature requires that it give up about 4.2 kJ/L/°C (this is called the heat capacity of water). So, let's say your tap water is 10 °C. So, for every liter of water that falls on your trees from the sprinkler, it's going to take 42 kJ to cool it down from 10 °C to 0 °C. Freezing that water requires that it give up more energy, called the heat of fusion, to change state from a liquid to a solid. The heat of fusion of water is about 334 kJ/L. So, each liter of 10 °C tap water from your sprinkler that falls on the trees has to lose a total of about 376 kJ of energy in order to turn to ice. That's actually quite a significant amount of energy, enough to power a 60 W lightbulb for over an hour and a half. Nature has to take that much energy away from the thin layer of sprinkler water that's coating the plants before any of the plant tissue will start to freeze, causing damage. Unless it's very very cold outside, the sprinkler water isn't going to lose enough of its energy fast enough for the plants to receive damage.
