Simply putting it in the freezer won’t make it cold faster. Ambient temperature doesn’t drive heat transfer. What you need to do it wrap that sucker with a wet paper towel.
Haha, it's basically a stronger version of a mimosa which is traditional to drink with breakfast on Christmas morning (it's also the name of a UK band who won Eurovision but the less said about that the better)
The, uh, cold never bothered me anyway