North of the Alps temperature would drop considerably. South of the Alps, probably fine due to the thermal mass of the mediterranean sea. However, for the whole Europe you would see a massive drop in rainfall, since basically all the humidity comes from the Atlantic's warm air that carries a lot of it.

Additionally, Carribeans, Mexico and South of the US would also be fucked since the energy wouldn't disperse and all the heat and humidity would stay there. Hurricanes would be much more violent, with way more rain, and likely more frequent.

Labrador current might become weaker though, but it is not a given. Currently, the waters from the gulf stream cool down and sink to the bottom of the ocean, so they don't displace the artic waters and hence are not likely the cause of how cold north eastern US is.