Ice in the freezer can absorb smells from both the freezer and the refrigerator, to the surprise of many people. Ice can also sublimate (evaporate) and shrink fairly quickly. So you can either place your ice in a sealed bag/container, and/or do the same with your food.
In my fridge/freezer situation, I don't leave any food unwrapped so that the ice never absorbs food smells. I used to stick leftover pizza in the box in the fridge and by the next morning my ice would taste ever so slightly of it, so now I put the pizza in a Tupperware-type container. There doesn't seem to be any problem with uncooked vegetables stored in there (not smelly onions or garlic or anything), but cooked food is problematic.
For ice that you're going to be storing, I recommend either Ziplock style sealed bags or Tupperware-style containers. Those keep it sealed from sublimating and from absorbing smells. Easy.
If you want to see just how permeable ice is, add a drop of food coloring on top of a big block and watch how it flows into the cube along invisible cracks.
To read all the ice posts here on Alcademics, check out the Index of Ice Experiments.