Does salt on the snow and ice covered roads and sidewalks make the nearby air temperature cooler?
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!