Both cases are the same.
The beer is just a fraction OVER its freezing point (which is below zeroC because of the alcohol, but not much below zeroC).
The lime (or taking the top off) causes the CO2 to come out (fizz).
This takes energy - and the only place that the energy can come from is a temperature drop.
Therefore the beer ices.
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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