from my own experience: sparkling wine, champagne, beer or other drinks containing CO2 expand more during freezing than liquids without CO2, which can lead to cracked bottles (if glas) or at least leaks at the lid ending up with a lot of frozen liquid in the freezer. Especially with champagne, although I haven't tried it, it gets worse because the pressure is much higher than with beer and the bottles are really closed. Do not try it at all! I think my father had once an exploded bottle of champagne in his freezer. He needed to clean everything because of the glas and odeur! Even, if everything went well, the sparkling character is clearly lost for drinks like cola or lemonade.
With wine it's a bit different. Here it definitely depends on the lid and if the bottle is horizontal or vertical frozen. If it's layed and has a screw-on lid (which has become more and more common in recent years, at least in my wine region), you can be lucky and only a few mL will leak out, but usually the bottles remain intact. The liquid that leaks is the one that freezes last, because it contains the sugar, the aromas and the alcohol. Or the other way round: water freezes first. So if all the liquid has remained in the bottle, it makes no difference for most of us, but please let it thaw completely before pouring it into your glass. If some liquid has leaked out, just try the wine and if it doesn't taste the way you like/expect it, you may still be able to use it as an ingredient in your next sauce.
With cork, i don't have so much experience, but the cork will be pushed out a bit (if possible, so no plastic coverage arround), but very likely prevents leakage.
In summer I often forgot to take the wine out at the right time (before freezing), so I ended up with something like a slushi made with wine. Just shake it thoroughly until you get a nice mixture, then pour it into a glass. You will see, it thaws faster than a bottle of water. This is for white or rose wine. Ok, maybe you should not do something like this with high quality or rare wine. You can also improve it and make a nice looking cocktail out of it, fancy, he?
After few bottles forgotten in the freezer, i made a little magnetic batch, which i pin on the door. So, everbody who sees it, opens and checks. Since then, the amount of forgotten bottels decreased significantly!
I don't drink red wine, but is there a reason why you should drink a really cold red wine?
However, with cooking, there will be a difference, because all the volatile aromas will disapear as well as some of the alcohol. Of course, it depends on the duration and the heat.
Long storage in a frozen state is not advisable. But as long as all the liquid remains in the bottle, it is not a problem, at least for bottles with screw caps. With the cork, I guess it depends on the interaction between the cork and the temperature. It is possible that at least the inner part of the cork will dissolve a little when the bottle is opened and that cork crumbs will end up in the wine.