Here is the short version as I understand it: put the water first and then the ice. Depending on how much alcohol the ouzo has it will react differently to extreme cooling. Don’t overdo it cooling this drink because you then kill the aroma.
And here is the long version:
“Anethole is a rather nonpolar compound. The solubility of the ancthole contained in the Greek liqueur Ouzo is in a range in which the compound crystallizes out in the deep cold whereas it is still soluble in the beverage at room temperature. This effect can easily be observed in a Greek restaurant. When Ouzo is served as a well-chilled aperitif it appears cloudy due to precipitated ancthole crystals. On standing and warming, the cloudiness disappears by dissolution of ancthole in the aqueous ethanoL There is no other
flavour component in Ouzo which undergoes this change. Therefore, it can be used for a simple selective separation of ancthole just by filtration of the cold liqueur. However, it should be kept in mind that ancthole has a rather low melting point of 22 °C\ This has to be taken into consideration during any separation operations. All equipment used for filtration h3s to be precooled to avoid loss of ancthole by liquefaction.
It is not to recommend to cool the liqueur still more than described here because then water ice also begins to crystallize. If you cool several brands of Ouzo you will find that the degree of crystallization of ancthole is different, which gives a hint about its varying content in the liqueur.
Λ 500 ml volume of Greek liqueur Ouzois allowed to cool in a deep freezer at -20 °C overnight. The viscosity of the solution increases. Anethole crystallizes in the form of colourless leaflets, A sintered glass filter funnel is precooled in the same freezer and used for the filtration operation. The Ouzo is filtered by suction, which requires 30 min because the glass filter easily tends to become blocked by the ancthole crystals. To avoid this, it is to recommended to scrape of] the material from the filler surface occasionally by means of a pre-eoolcd spatula. During filtration, the temperature at the funnel should not rise above -12 °t. Finally, a colourless crystalline mass (300 mg) is scraped out of the sintered glass filler funnel, put into a glass vial and immediately evacuated with an oil pump at 20 Pa and 15 °C to remove traces of water and ethanol Colourless crystals of pure anethole (150 mg) remain in the vial, which, depending on the storage temperature, can be kept as a solid or a liquid.”