If a body at temperature A is put in contact with a body at temperature B such that the temperature of the body A is higher than that of temperature B, then heat energy will flow from body A to body B until the temperatures of body A and body B are equal and no heat energy flows between them.
If you just put the ice cubes in the drink, let's say they're exactly 0 and your drink is 20 degrees. Then upon equilibration your drink is 18 degrees (say) and the ice cubes have melted.
If you put the whole lot in the freezer, at -15 degrees, we'll assume your freezer acts as a temperature resevoir, that is, its temperature doesn't change no matter what you put in the freezer, then your drink will keep cooling until its temperature is the same as the freezer, which in this case is -15 degrees.
So the freezer will undoubtedly make your drink cooler. You basically answered your own question when you said the ice cubes wouldn't melt as fast in the drink in the freezer. Why? Because the drink will be cooler...
In terms of speed, if you consider some simple models such as Newton's law of cooling or Fourier's law, they're proportional to the temperature difference, and so the larger the temperature difference, the faster the cooling. Therefore the freezer wins again.
Physics gets a bit more complicated when things change phase (ice to water to steam and vice versa) but in general the above holds.
post edited by sillynarbie - 2014/11/28 12:45:16