Freezing air temperature
Freezing or frost occurs when the air temperature falls below the freezing point of water (0 °C, 32 °F, 273 K). This is usually measured at the height of 1.2 metres above the ground surface. There exist some scales defining several degrees of frost severity (from "slight" to "very severe") but they depend on location thus the usual temperatures occurring in winter. The primary symptom of frost weather is that water freezes. 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 done to prevent this from happening. Terminology. The English word "frost" has 2 base meanings that are related to each other but nevertheless sufficiently different: The WMO avoids the word "frost" alone and uses Relation between freezing and hoar frost or ground frost. A temperature at or below freezing is not absolutely necessary to get ground frost or hoar frost; they can form even if air temperature is marginally above freezing point if the sky is clear. This is because the ground loses heat due to  radiation. It radiates its heat to the sky/space. 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 a clear night the ground can become colder than the air because it radiates its heat to the sky, and ground frost can form. On the other hand, a temperature below the freezing point of water does not mean that  hoar frost must occur.