Differential centrifugation is the standard and very common method used to isolate exosomes. This method combines ultracentrifugation with sucrose density gradient. Freezing steps sometimes influences exosome structure and functionality. For more details , please see the attached files.

The freezing of cell culture medium might decrease the exosome yield and increase the amount of contaminant proteins significantly.

if you mean alteration in the exosome structure in terms of their morphology then it shouldn’t be a concern but the content of exosomes could get affected due to freezing the medium prior to use which could further affect the functional assays.

Article Isolation of Biologically-Active Exosomes from Human Plasma

this article might be helpful, they have tried to do a comparison between fresh and frozen plasma.

Hope it helps.

Cheers !