I did this with a bottle of Liquid Farm last summer. I let it get slushy again, put a long straw in it, had it for lunch. Nikki approved 
I think lots of folks here regularly freeze wine if they can’t take an entire bottle down. I do it on occasion. Works fine. Sometimes have to strain the wine. Especially when I need a cup of wine for cooking … and don’t want to use one of my wines. And I don’t particularly want to drink the wine I’m cooking with.
J
Freezing a wine could cause Potassium Bitartrate to precipitate out, which would lower the wine’s TA and raise or lower the Ph (depending on if the ph is above or below 3.6, strange as it may sound)…which would make the wine taste less tart. I’ve heard that P BT precipitation can take colloides with it…colloides mostly affect the texture of the wine.
So it depends on the wine and how much P BT is in the wine. White wines can be cold stabilized to deal with this before leaving the winery…but reds never become cold stable. I suspect the changes are, generally, subtle enough that you’d only notice it by tasting a bottle that was frozen next to one that wasn’t.
Freezing a wine that has a Ph of 3.8 (not unheard of) would push the Ph higher (if there’s P BT precipitation), which might affect the wine’s ability to age. Also, high Ph wines can be soapy, so that might become more of an issue.
That’s my understanding anyways.