Freezing traditional Greek dishes

Some of the volatile flavors will be diminished, but I've managed to make fairly good drinks with the help of mint that I kept frozen. In my experience, freezer burn starts to become visible after two or three months, and starts to harm flavor probably around 4-6 months.

I'm not sure preparing the drink will work really well, but if you just defrost the drink in the refrigerator, it probably won't be terrible. Active thawing with heat will probably cause some harm. Many infusions and teas become a bit cloudy and lose color after bottling or freezing, which is why most bottled teas use an enzyme (not usually a listed ingredient) designed to mitigate that.

The best way to freeze something is to do it fast. Chill the food first in the refrigerator before putting it in the freezer. Keeping the food thin/flat rather than thick will help the center to chill faster. Loading up a sheet pan with individual portions works well for this - just be sure you have room for it in the refrigerator and freezer.

However, the larger problem with this type of sauce is re-heating of it - the sauce tends to split into its constituent ingredients. Reheating the sauce very slowly on low heat is the best way to prevent the splitting. You can also consider adding some lecithin to the sauce during cooking, which will help stabilize it. See How can I reheat a roux-based (alfredo) sauce in the microwave without separation? and Keeping A Sauce From Separating for details.