I like my drinking water at room temperature but I like all my soft drinks (soda, pop, etc) icy cold. We have a separate freezer and have room to store a bag of ice from the supermarket. BF (before freezer) we were limited to the little space above our fridge.
I found that the door shelves of the freezer were pretty darn useless for just about anything. I bought a long, narrow plastic container that squeezed into one shelf. We would empty the ice cube trays into the container, and then refill them. As we used the cubes from the container the water in the trays had a chance to freeze.