You can simply dissolve your isolated exosomes with PBS preferably containing protease inhibitor and freeze at -80 degree centigrade for a long time storage. I don't see a problem using DMSO which is used for freezing cells as a cryoprotectant.
If you need your exosomes for functional studies or EM imaging, better do not freeze them. It's better to perform your assays shortly after production and purification.
Dissolving in PBS and keeping in -80 should be fine. They are not alive creatures to need DMSO that you need to culture later. They are only bilayer vesicles.