I'm going to put athletic ice packs in my office freezer
I don't see anything wrong with that? Do you?
I think that's one of the best ways to keep food fresh and I need them for my injury.
If you're allowed to put stuff in the freezer, then do so. Just let your coworkers know beforehand.
I can do whatever I want with my things.
Yes you can but it's best to let them know before hand to avoid confusion.