Would freezing affect the flavour of mint tea?
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.