This very specific question that came after saw I a travel episode where they served alcoholic beverages in ice glasses in an ice bar. I wondered if the drink contents would stay in the glass (of ice) without the glass (of ice) melting. I reason that the drink would be cold enough to not melt the ice thus allowing it to stay frozen.
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.)