Can the temperature of a body become lower than the temperature of the surrounding air? In winters, frost is formed on the grass and wood and not on concrete roads.Temperature of frost is lower than the temperature of the surrounding air.So a question arises ""Can a body become colder than the environment"" or  there is something which I have misunderstood?
 A: Frost is formed overnight, while the temperature of the air is below the freezing point. However, it does not immediately disappear as the temperature of the air rises, as some time is required for the sufficient amount of heat to be transferred to melt the ice/snow (see latent heat).
In this sense, an even more striking phenomenon is the winter snow that persists for days or weeks in Spring, after the temperature goes above the freezing in daytime; see Snowmelt.
Remarks

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*The premise of the question is that the second law of thermodynamics prohibits transfer of energy from a colder object to a hotter one/environment without external work done. In this sense, the human body on a hot day or refrigerator are poor examples, since there the cooling is achieved via such external work.

*A comment below pointed out that we can have condensation on cold objects, even with the temperature of air above the freezing point. To some extent this has been already mentioned in the context of snowmelt (for those who followed the link), but it is still worth acknowledging explicitly.

A: A prima facie example of cooling below the air temperature due to evaporation is the wet-bulb temperature, that is, the temperature of a thermometer surrounded by a wet cloth or similar material. As the water keeps evaporating, the thermometer indicates a lower temperature than a thermometer without such wet material.
The measured temperature difference is used to measure air humidity in meteorological stations. If the air is saturated with water vapour (100% humidity), the temperature difference will be zero because no evaporation and cooling happens.
A: If conductive/convective heat transfer is low, then radiative heat loss can cool an object below the temperature of the surrounding air. As discussed in the answers to What is the temperature of the clear night sky from the surface of Earth?, the temperature of the night sky can easily be lower than the surface air. This has long been used to create ice in the desert at night.
If the air is dry and the object wet, then evaporation can cool an object below the surrounding air temperature. This is how earthen pots can keep their contents cool and how perspiration keeps humans from overheating.
See also the answers to How does frost form above freezing temperature?, Why does ice form on bridges even if the temperature is above freezing?, and Why does the windshield of my car freeze even if the outside temperature is above freezing?.
Some references to research, etc.
For those who who would like to read further on this, there is a large related research literature.  For just one example in the natural world, both energy balance modelling and observation show that leaves of subalpine herbs can have frost episodes even when the air temperature is above freezing. (Thanks  @Vladimir-F-Героям-слава).
To understand the potential of radiative cooling, an important number to keep in mind is that the power radiated by a $300\ K$  blackbody is
$$W=\sigma T^4\approx 450\,\ \textrm{W/m}^2$$
which is almost half the maximum solar irradiance at the Earth's surface of $\sim 1 \,\ \textrm{KW/m}^2$.
If the sky is transparent to a significant fraction of the spectrum of blackbody radiation, significant cooling is possible. The peak of 300 K blackbody radiation is $\sim10$ microns, and happens that the atmosphere has a large transparency window for 8-13 micron infrared wavelengths.
It was originally thought that such radiative cooling was only significant in deserts or at high altitudes, but with carefully engineered thermal photonic materials that reflect almost all visible light, but radiate strongly in the infrared atmospheric transparency window, it is possible to passively cool objects below ambient air temperature even in direct sunlight at sea level.
This is of great environmental and commercial interest, and although I am not sure what the current record is, one study made a theoretical estimate that temperatures as much as 60 °C below ambient is achievable, and an average reduction of 37 °C was been observed over a 24-hour cycle in populous area at sea level.
Even just using special ultra-white paint can keep surfaces 11 °C cooler than ambient at night and 4 °C cooler under noon sunlight. (Thanks @AccidentalTaylorExpansion.)
