It seems that there are no contradictions in all those statements.
Some people say it's an adiabatic expansion.
What they probably mean is that the initial expansion of the coolant at the output of a throttling device does not involve heat exchange with the surroundings, i.e., the cooling occurs due to evaporation - not due to the cooling effect of some external agent.
other say it's something related to the nozzle
This is a reasonable statement. A nozzle, as a throttling device, restricts the flow of coolant, which causes pressure drop.
According to me, pressure drop of the gas, takes the gas to its
boiling point. Since the boiling point of the gas is very low, cooling
takes place.
This is a reasonable summary as well.