" Is it possible to measure Impedance with an ohm meter.

No.

For example can you measure the Impedance of a 4 ohm
car speaker with an ohm meter?

No again it is a AC measurement as you say and an Ohm meter measures DC
resistance ONLY

When I tell people they cannot measure Impedance with an
ohm meter, you need an impedance meter and the impedance
must be measured with the speaker in operation, with a signal generator
supplying a fixed frequency,

Slightly incorrect the measurement of a speakers impedance is a average over
the frequency range of the expected use of the speaker.

when I tell him an ohm meter can only measure the resistance
of the coil there is always disagreement.

Huh they are wrong.

Steve