Ok, so I got impatient. Initial test results are in.
Half a bottle of Fruity Pink Wurzel went in the freezer for around 36 hours, the other half stayed down the cellar. This was a very young wine, only bottled in the last fortnight. I removed the frozen one from the freezer last night, marked it with a piece of tape and stood it next to its counterpart.
This evening I took 2 identical plain glasses, fixed an identical little square sticker in the centre of each foot and marked one with a tiny blue dot. I poured equal measures into each glass, frozen and thawed wine in the glass with the blue dot, checked their temperatures which were identical at 11.5°C, placed them both in front of Mrs. Mole, turned my back and told her to switch them around a few times so I wouldn't know which was which and then we both took sips from both glasses.
One of them had an immediate and fairly harsh mouth feel and left a slightly sharp aftertaste, the other seemed smoother or lighter but left a much nicer finish. We both preferred the same glass. Emptied and turned over, it had a little blue dot.
This warrants further experimentation.