Unless your freezer is unusually cold, the rum will not freeze. Because it doesn't freeze, there is no risk of the bottle shattering as the liquid expands during freezing.
'Gin won't freeze, given that it's ABV (alcohol by volume) is 37.5%,' she continued. 'So storing it in the freezer is absolutely fine. ' Reducing the temperature of gin helps softens the alcohol perception on the taste, making it much easier to drink and enjoy responsibly.