I noticed when it snows and salt is melting the snow on the roads in the city, that the air temperature feels a lot cooler than the temperature indicated on the thermometer. A 40 degree fahrenheit temperature feels like 30 degrees. Is it the moisture from melting snow or rain that makes the air temp feel ten degrees cooler or is it the salt brine (melted snow or ice and salt? Is it similar to adding salt to the ice in an Hand powered ice cream churn to make the cream container colder to make ice cream?
As water melts due to adding a salt (AKA melting point depression), it absorbs energy from the environment and the temperature of the salt/ice/water mixture does, indeed, drop. Whether that is sufficient to cool the air above the ice perceptibly, though, is a matter of opinion.
Another effect that might make the air feel colder is increased humidity, particularly as the salt slush is splashed into the air by vehicles.
You could perform an experiment yourself to determine the air temperature above two containers, one with fresh snow and the other with snow and salt. If you do, please post your results as an answer!
It depends on the exactness of your thermometer and your definition of ‘nearby’.
Since adding salt to ice causes the overall mixture to assume a liquid phase rather than the previous solid phase, melting enthalpy is required to liquefy the ice/salt mixture. This melting enthalpy is typically supplied by drawing heat from the surroundings, i.e. due to the melting everything gets colder. This, naturally, also draws heat from the surrounding (close) air. However, there are no direct effects on the surrounding air.
You can read more about the effect of salt added to ice in this question.