I intended to slightly chill a red wine in the fridge (not the freezer) for a couple of minutes and forgot it for a week because of an emergency distraction. Is it kaput?
No. Any rumours of its death would be highly exaggerated. Red wine is just as sturdy as, and in some ways more sturdy than, white. Cold merely slows down reactions responsible for aging, so consider your wine better preserved.
The only issue to worry about is freezing, which would only occur if your fridge is seriously malfunctioning. Frozen liquids expand, and that could drive out the cork or distort the screwcap, but you would have noticed that. And it would take a temperature below minus-6 C to do that (alcohol reduces the freezing point of wine).
One issue that does not apply to your situation but which others might want to keep in mind is a desiccated cork. Fridge compartments are very dry. Were you to forget the wine for many months, the cork could start shrinking. That could cause leakage and/or permit corrosive oxygen to enter. It may not kill your wine, but at the very least you should take care in pulling the cork, which might break.
A final caveat: You should be prepared for the possibility of crystalized sediment that looks like tiny shards of glass, which may float around or stick to the cork's bottom. Sometimes called wine diamonds, these particles are made of potassium bitartrate, which forms when potassium bonds with tartaric acid, both naturally present in grapes. Perfectly harmless, the compound – commonly known to cooks as cream of tartar – precipitates out of solution because of the temperature change. You generally don't see the shards in white wines because many producers, knowing those wines are destined for the refrigerator, cold-stabilize before shipping.
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