If the temperature is low for sufficiently long time, freezing will occur with some delay in lakes, rivers, and the sea.
It can occur even in water supply networks, although this is highly undesirable and efforts are made to prevent this from happening.
The amount of heat that radiates is proportional to the difference of the fourth power of the temperatures between the two objects.
At night, the atmosphere is not being warmed by the sun and the sky/space can approach 2.7 K (the blackbody temperature of the cosmic microwave background radiation).
On the other hand, a temperature below the freezing point of water does not mean that hoar frost must occur.