Hi georgie339,
The zoos in the Chicago area generally require a bachelors or an intent to complete one to apply. The internship programs are competitive and require application and a 6 week, 40 hrs a week commitment, at least.
It's not a bad idea, if you plan to take a gap year, or want to work in a non-animal related area of the zoo. the zoos downstate (like Scovill)are not as picky.
I would recommend talking to your vet and seeing if there are LA vets that he is aware of in suburban or rural areas. Unfortunately, the ISVMA website lumps the LA and SA vets together, so they are not much of a help in finding an active large animal vet. If you live near a race track, or have relatives that live a bit farther south that do, you could contact them and get the names of vets that are in the area.
You may also want to call the cops. Chicago has a mounted police force. I'm not sure which precinct they are based out of, but they may have the name/s of vets that service their horses.
Unfortunately, since they are few and far between, you may need to take time out during a break to spend a week downstate or on the Iowa side of the state to get that experience you're looking for.