An air frost and ground frost are different, the temperature that meteorologists report is taken at or predicted for about 1.5-2m above ground, at night the surface temperature is often several degrees cooler at surface level. As such a ground frost can occur without the air (at 1.5-2m) ever reaching freezing point.
An air frost is where the temperature at 1.5-2m is 0°C or below, a ground frost is where the surface temperature is at 0°C or below.
This difference means that a ground frost threatens even when the reported/expected air temperature is several degrees.
Last night we got no ground frost, here in Tunbridge Wells, but the air temperature I recorded at 2m fell to 2.6°C at some point during the night (it was only 4°C at 7am). We were lucky not to get a ground frost.