Will a container made of ice hold an alcoholic beverage that is below freezing in an environment that is also below freezing?
Depends on the temperature and alcohol content. At 0°C, the container will definitively melt. 

Below, your container will melt from the inside until the liquor is diluted so much that its freezing point is raised to the current temperature. (Or the other way round, water ice precipitates from your booze, concentrating it until its freezing point has dropped to the temperature of the surrounding.)

You can easily calculate the equillibrium alcohol content for a given temperature, https://en.wikipedia.org/wiki/Freezing-point_depression#Calculation
(The result will be slightly off, because this calculation is derived for infinite dilution.)