I cannot give a definitive answer as it depends on the properties of your samples, and how the NanoSight information fits with any other investigations you are performing.
You would need to test if the process of freezing at -80oC changes the sample data compared to that obtained on a fresh sample – do any particles present aggregate on freezing/thaw or are particles destroyed, for example.
Do you typically use the spent media in other experiments with different techniques? Would you normally freeze the samples before using in these techniques? If so then it is more appropriate to freeze the samples and then measure with NanoSight so your data comparisons are more appropriate.
If you are interested in measuring exosomes, extracellular vesicles etc, we know that -80oC can cause a decrease in the number of particles measured for some samples. But for other tests on the samples it is not possible to use fresh samples so the researcher measures the fresh sample just before freezing, freezes aliquots and then tests a part of the thawed sample when it is used in other methods.